Compendia like the one you attach are extemely deceptive. Let's have a look at the ACTUAL status of this opinion in historical context.

Firstly, it's incorrect to conflate BoB and BoD.  St. Robert Bellarmine admits that the Fathers were divided on BoD, and some of the Fathers who accepted BoB, rejected BoB, often in the same sentence.

In favor of BoD, you can find only 2 Fathers (even those are debatable) who may have been constructed as "supporting" BoD:  St. Augustine and St. Ambrose.  Of these two, St. Augustine floated the idea very tentatively in his youth but then forcefully retracted after he had cuts his teeth battling the Pelagians, and some of the strongest anti-BoD statements in existence come from St. Augustine.  St. Ambrose, on the other hand makes a comment that could be read several different ways, but elsewhere rejected the notion, in his work De Sacramentis.

Read here regarding the change in St. Augustine:
https://catholicism.org/baptism-of-desire-its-origin-and-abandonment-in-the-thought-of-saint-augustine.html

When he first floated the idea, he said that he had gone back and forth on it, but then said, "I find ...", indicating that this was clearly his own personal speculative opinion and not something he had received from the Apostles.  But then I invite you read the above about how, after battlinng the Donatists and Pelagians, he realized the Pelagian implications of BoD.  St. Augustine engaged in a lot of theology right out of the gate, but then had to issue an entire book called "Corrections" later in life to correct his mistakes.

With regard to St. Ambrose, he taught elsewhere:

Duties of the Clergy
“'Unless a man be born again of water and the Holy Spirit, he cannot enter the kingdom of God.'  No one is excepted: not the infant, not the one prevented by some necessity.”

De Mysteriis
"Nor on the other hand is there any mystery of regeneration without water: for ‘unless a man be born again of water and the Spirit, he cannot enter the kingdom of God.’ [John 3:5]  Even a catechumen believes in the cross of the Lord Jesus, by which also he is signed; but, unless he be baptized in the name of the Father and of the Son and of the Holy Spirit, he cannot receive the remission of sins nor be recipient of the gift of spiritual grace."

So, did he contradict himself or change his mind?  If you look at what he said about Valentinian, St. Ambrose states that he hopes that those such as Valentinian could be "washed, but not crowned," stating that not even those who are martyred without having received the Sacrament are "washed, but not crowned."  I believe that he meant that they could be washed of the punishment due to their sins but not received the Beatific Vision (not be crowned).

So you have 1/2 Father (early St. Augustine vs. late St. Augustine) and MAYBE (but IMO unlikely) St. Ambrose.

On the other hand, you have in the AGAINST BoD camp the following Fathers:

Late St. Augustine, Fulgentius (St. Augustine's disciple, clearl carrying forward the later opinion of St. Agustine), Tertullian, St. Cyprian, St. John Chrysostom, St. Cyril of Jerusalem, St. Gregory of Nyssa, and St. Gregory nαzιanzen ("the Theologian").

cited in the link above (can be found elsewhere):

Testimony of Three Theologians

Before supplying Saint Augustine’s retractions I will quote three modern theologians to demonstrate the lack of unanimity among the fathers who raised the question directly or indirectly concerning baptism of desire: Fathers William A. Jurgens, Bernard Otten, S.J., and Karl Rahner, S.J.

Father Jurgens: “If there were not a constant tradition in the Fathers that the Gospel message of ‘Unless a man be born again . . . etc.’ is to be taken absolutely, it would be easy to say that Our Savior simply did not see fit to mention the obvious exceptions of invincible ignorance and physical impossibility. But the tradition in fact is there, and it is likely enough to be so constant as to constitute revelation.” (Jurgens, The Faith of the Early Fathers, Vol. 3, pp. 14-15, footnote 31, my italics)

Next, Rev. Bernard Otten, S.J., one-time professor of both Dogmatic Theology and the History of Dogma at the University of St. Louis, Missouri, in his Manual of the History of Dogma wrote: “Baptism of water, although ordinarily necessary for salvation, may be supplied by martyrdom, and under certain conditions also by the baptism of desire. The former was universally admitted, but the latter was apparently denied by Chrysostom and Cyril of Jerusalem.” (Vol. I, pg 351)  Abbot Jerome Theisen, O.S.B., in his book, The Ultimate Church and the Promise of Salvation, affirms the same of Saint Gregory nαzιanzen and adds Saint Basil as being opposed to the speculation.

And, lastly, Rahner:

“. . . we have to admit . . . that the testimony of the Fathers, with regard to the possibility of salvation for someone outside the Church, is very weak. Certainly even the ancient Church knew that the grace of God can be found also outside the Church and even before Faith. But the view that such divine grace can lead man to his final salvation without leading him first into the visible Church, is something, at any rate, which met with very little approval in the ancient Church. For, with reference to the optimistic views on the salvation of catechumens as found in many of the Fathers, it must be noted that such a candidate for baptism was regarded in some sense or other as already ‘Christianus,’ and also that certain Fathers, such as Gregory nαzιanzen and Gregory of Nyssa deny altogether the justifying power of love or of the desire for baptism. Hence it will be impossible to speak of a consensus dogmaticus in the early Church regarding the possibility of salvation for the non-baptized, and especially for someone who is not even a catechumen. In fact, even St. Augustine, in his last (anti-pelagian) period, no longer maintained the possibility of a baptism by desire.” (Rahner, Karl, Theological Investigations, Volume II, Man in the Church, translated by Karl H. Kruger, pp.40, 41, 57)

Rahner might also have included others among the fathers who denied the possibility of salvation for the unbaptized catechumen who died before receiving the sacrament.

Karl "Anonymous Christian" Rahner at least had some intellectual honesty, as he would have loved to find the Fathers supporting his opinion, but he admits that they did not.

Unfortunately, too many Trads don't have that same honesty as the Modernist.

1) they conflate BoB with BoD (and list BoB Fathers as supporting BoD even when many of them clearly state that the ONLY alternative to Baptism in water is martyrdom)

2) they have even gone so far as to lie and claim that the Fathers unanimously supported BoD.

St. Robert Bellarmine himself concedes that the Fathers were at best divided on the matter of BoD.

Thus, there's no evidence whatsoever that BoD was revealed teaching handed down from the Apostles, or otherwise, you would have found broad Patristic consensus and some statements to the effect that this teaching had been received from the Apostles.

With regard to BoB, most Fathers did believe in it.  As far as can be discerned, and we have also the testimony of St. Augustine, the idea originated with St. Cyprian.  St. Augustine, again, cited St. Cyprian not as having received this teaching but as having based it on various arguments.  Recall that St. Cyprian promoted a doctrine regarding re-baptism that would later be declared heretical by the Church.

Interestingly, though, when St. Cyprian refers to those who received this "BoB" (he didn't use the exact term) as having received the SACRAMENT of Baptism.  This has been written off as a mistake.  But was it?  At one point St. Cyprian referred to such as these having been washed in their blood while the angels pronounced the words.  This gives us a clue that what he was thinking was that in martyrdom the martyr's blood could supply for the water, while angels pronounced the form ... thus resulting in matter + form and the Sacrament of Baptism, confected extraordinarily with alternate matter and and alternate minister.

Some references to "Baptism of Blood" refer to people who were known to have been baptized, such as the priest Lucian.  What was meant by this "Baptism of Blood," was a second baptism where all their sins were washed away, and thus the Catholic teaching that martyrs go straight to heaven.

St. Ambrose refers to unbaptized martyrs as "washed but not crowned," again, where their sins are washed away but they do not enter the Kingdom (are not "crowned"), i.e. do not enter the Beatific Vision.

During times of persecution, the Church ordered that all catechumens should be baptized.  Why?  If martyrdom was a Baptism, why was this necessary?

This also could easily explain some references to the Saints who were said to be martyred catechumens.  Those who had been emergency baptized during times of persecution were nevertheless still considered catechumens, as they had not completed their instruction, and were not admitted to Holy Mass, Holy Communion, or the other Sacraments until the normal course of their instruction had been completed.

When we get to the Council of Trent, we'll see that if one wants to read Trent the way proponents of BoD do, Trent actually rules out "Three Baptisms" and rejects a "Baptism of Blood" that does not reduce to a "Baptism of Desire".  But we'll come back to that later.

So, after St. Fulentius, disciple of St. Augustine, rejected BoD, we have NO MORE MENTION of the subject again until we find it resurfacing in a pre-scholastic debate between Abelard (who rejected it) and Hugh of St. Victor (who accepted it).  That's where the story resumes, and I will come back later as I have more time to pick up from there.

But thus far we find the following:

1) no evidence (by way of Patristic dogmatic consensus) of BoD being revealed doctrine

2) majority of Church Fathers rejected it (Tertullian, St. Cyprian, St. Cyril of Jerusalem, St. John Chrysostom, later St. Augustine, St. Gregory of Nyssa, St. Gregory nαzιanzen ("the Theologian"), St. Fulgentius

3) only early St. Augustine promoted the idea, but he proposed it very tentatively and obviously as his personal speculation, but ...

4) later St. Augustine retracted it and issued some of the strongest anti-BoD statement in existence

5) St. Ambrose referred to what may be construed as a BoD, but stated that one could be "washed but not crowned" in such a scenario, and elsewhere denied that even good catechumens could be saved without the actual Sacrament

6) Pope St. Sirius (dogmaticaly?) affirmed that each and every one of those desiring Baptism, yet prevented by some necessity, cannot enter the Kingdom of Heaven

7) many Fathers accepting (and none known to reject) a Baptism of Blood, but ...

8) St. Augustine attributing the notion to St. Cyprian's argumentation (rather than to received teaching)

9) some ambiguous references, as they referred to people who had been Sacramentally baptized already

10) St. Cyprian calling BoB a Sacrament, stating that the martyr's blood supplied for the water (the matter) while the angels pronounced the words (the form) ... thus suggesting it was just an alternative extraordinary mode of receiving the Sacrament (rather than some extra-Sacramental exception)

11) St. Ambrose stating that even the martyrs are "washed but not crowned" (i.e. have the punishment of their sins remitted but cannot enter the Kingdom of Heaven)

12) the Church ordering the baptism of all catechumens during times of persecution (why if there's a BoB?)

13) with these early-baptized catechumens still being considered to have the status of catechumen (thus explaining reference so the martyrdoms of "catechumens" considered saints)

So THIS HERE is the accurate characterization of the status queaestionis in the early Church.  Compare that to the statements of those Catholic theologians and also even Karl Rahner.

As I said, I'll resume the story then with the debate between Abelard and  Hugh of St. Victory, the next time after St. Fulgentius (disciple of St. Augustine who rejected BoD) this subject is found to have been brought up in Catholic sources.

I do not wish to engage in arguments from magisterial texts which implicitly refute BoD in this thread. The reasons are that we believe doctrines because the Church teaches them, not because we can conclude them ourselves and I've already looked into those arguments.

This is where a BOD fails every time - it fails at actual, authoritative Church teachings every time, as well as Scripture.

IMO, the only way  BODers who want to refute the non-BODers stand a chance of "converting" them, is to use those same "magisterial texts" to prove a BOD rather than ignore them, or have no authority in this matter.

Yes, this is what I contend also.

St. Robert Bellarmine limited it to FORMAL catechumens.  There's no evidence ANYWHERE that this "BoD" can apply to anyone other than a catechumen ... if you don't count the wishful thinking of various Modernists and neo-Pelagians.  Extension of BoD beyond Catechumens guts Tridentine Catholic ecclesiology, which is why when St. Robert asked the question, it was explicitly formulated as, "whether catechumens ...".  As even Rahner admits, the Church Fathers rejected the notion that anyone could be saved without visible adherence to the Church.  Catechumens had a visible and formal connection with the Church, an official status, as when they became catechumens they were marked with the sign of the cross and were called "Christian".

Nevertheless, the evidence is strong that not even catechumens can be saved without the Sacrament of Baptism.  One of the Church's dogmatic EENS definitions clearly states that there's no salvation "outside the Church of the faithful (fidelium)".  As Msgr. Fenton admits, the term fideles has always been a technical theological term that excludes catechumens (thus in the early Church, you had the "(part of the) Mass of the Catechumens" and "(part of the) Mass of the Faithful"), and he cites the history of this term.

As we saw, the majority of the Church Fathers rejected salvation by BoD for catechumens also ... including even St. Augustine (in his post-Pelagian period, as proven by the catholicism.org article, and as conceded by Rahner) and St. Ambrose (in De Mysteriis where he states that catechumens who died without the Sacrament cannot enter the Kingdom of Heaven).

I do believe an an "analogous" Baptism of Desire, one which can "wash" the (punishment due to) sin, but which does not suffice for entry into the Kingdom, i.e. the Beatific Vision.

So what do people make of the teaching of Pope St. Siricius where he says that each an every one of those who dies, while desiring Baptism but prevented by necessity, cannot enter the Kingdom?  Please explain.  As with a lot of issues, people cling to evidence that favors their position and ignore ("filter out") evidence that militates against their opinion.

This teaching from Pope St. Siricius EXPLICITLY rejects that the desire for Baptism suffices for someone to enter the Kingdom when they are prevented by some necessity from receiving the Sacrament of Baptism.

So after St. Fulgentius (died A.D. 533), the next mention of BoD we find in Catholic sources appears in the pre-scholastics, Abelard (d. 1142) and Hugh of St. Victor (d. 1141).

Abelard rejected Baptism of Desire, while Hugh of St. Victor prevented it.

Peter Lombard (d. 1162) was trying to decide between the two, so he wrote to St. Bernard to get his opinion.

St. Bernard sided with Hugh of St. Victor and then wrote (in 1130) in his Tractatus de Baptismo:

So, believe me, it would be difficult to turn me aside from these two pillars – I mean Augustine and Ambrose.  I confess that, whether in error or knowledge, I am with them; for I believe that a man can be saved by faith alone, provided he desires to receive the sacrament, in a case where death overtakes the fulfillment of his religious desire, or some other invincible power stands in his way.

So here we have St. Bernard admitting that the opinion could be erroneous, but that he was basing his opinion on the authority of Augustine and Ambrose.  Of course, St. Bernard was unaware that St. Augustine retracted the opinion, and his assumption that St. Ambrose believed in it was also IMO incorrect.  Unfortunately, St. Bernard also errs in this passage by promoting the notion of salvation "by faith alone".  And he also contradicts St. Augustine by asserting that the possibility that "some ... invincible power [could] stand... in ... [the] way" of someone receiving the Sacrament.  Really?  Some invincible power could prevent God from bringing the Sacrament to His elect.  Why does he contradict the same St. Augustine on that point?  Here we see two gross errors on the part of St. Bernard, and so it's not unlikely that he did in fact err also in promoting Baptism of Desire.

So, what of the other Church Fathers, who rejected BoD?  Were they just chopped liver?  We need to understand the context here that at this time there was a revival of interest in St. Augustine (more access to his writings), leading to an exaggeration of St. Augustine's authority, so much so that the Church needed to intervene and condemn the proposition that it is permitted to prefer a teaching of St. Augustine to the Church's Magisterium.  As the Church does tend to condemn propositions that no one holds, you can be sure that there were people out there who had this attitude.  And here too we have St. Bernard preferring the opinion of Augustine and Ambrose to the truth on the matter.

To add some additional context, St. Bernard was a diedhard opponent of Abelard, being a proponent of what has been termed "mystic theology".  St. Bernard vehemently rejected Abelard's approach of applying reason to matters of faith.  St. Bernard was in fact dead wrong, and Abelard's system was actually THE precursor to scholasticism.  In fact, one might say that Abelard was the father of scholasticism.  Please see my analysis of the situatioin here:
https://www.cathinfo.com/fighting-errors-in-the-modern-world/foundations-restored-a-catholic-perspective-on-origins/msg842251/#msg842251

Also, an interesting note is that Fr. Laisney in his screed against "Feeeyism" DELIBERATELY OMITTED the expression "whether in error or knowledge" from this quote from St. Bernard, replacing the expression with ellipses.  Gotta love the intellecual honesty from the BoDers here.

In any case, Peter Lombard went with St. Bernard on the BoD issue, and included the opinion in his work Sentences (1150), and that manual would heavily influence St. Thomas Aquinas and the other scholastics.  BTW, Lombard's book was based on Abelard's Sic et Non (Pro and Con), which was actually the foundation for scholasticism, that entire method of answering objections, etc. that St. Thomas was famous for.  Abelard invented that entire system and, though Lombard, it was picked up by St. Thomas.  This is the very methodology that St. Bernard condemned as being harmful to the faith and "sophistic".  St. Bernard was wrong.  And St. Bernard was wrong also about BoD.

From the Sentences, St. Thomas picked up on BoD, and from St. Thomas, of course, it "went viral," so to speak, among theologians.

Thank you very much Ladislaus. I am convinced neither St. Ambrose nor St. Augustine believed in BoD and St. Bernard falls with him too.

I expect the other quotes in the book will fall in a similar way.

After reading this thread and listening to some videos from schismatic-home-aloner I now tentatively lean towards rejecting BoD and BoB.

To clarify my thinking process lest someone think I'm making rash judgments. I have already read quite a bit on the topic and my intellect was convinced by the various arguments from Magisterial docuмents by the Dimonds, however, I rather thought that I reasoned incorrectly than that I reasoned better than St. Augustine, St. Thomas, St. Alphonsus, etc. etc.

What prompted me to reevaluate the issue was that Ladislaus and DigitalLogos, whose knowledge I respect, rejected BoD. Thank you both.

Now that I see the consensus I thought was there is crumbling rapidly and now that I'm aware of Pope St. Siricius' and Pope St. Leo the Great's teaching and other saints who rejected BoD, I can no longer defer judgment to the collective teaching of the theologians since there is no such thing.

I will continue to look into the matter and I hope to get the time to analyze each quote in the book and finally present a table for and against BoD.

God bless you.