Ironically, it is Fr. Pfeiffer in this old Angelus Article who points out the common teaching of the Church: Baptism of desire is de fide:

[Here is the link to entire article, in which additional Feeneyite errors are refuted: http://archives.sspx.org/miscellaneous/feeneyism/three_errors_of_feeneyites.htm]

"The idea that an individual died before he was able to receive the Sacrament of Baptism is equally curious, because it is God who determines how long each of us shall live to the second. And it is God Who in His most benevolent Providence grants Baptism to everyone who receives it. Is He a monster (for Whom nothing is impossible or difficult) who instructs certain individuals in the absolute necessity of Baptism, grants them the grace of wishing it, then cuts off their life so that they can never receive it? And then casts them into Hell forever for not having received it? No, on the very contrary. He is an all-loving God, Who most certainly provides to the responsive all that is needful to them. If they are truly desirous of Baptism, if need be, He will provide it, even by a miracle. (It is a miracle to us, but not to Him.) This is what the Scriptures means when it says, "The hand of the Lord is not shortened" (Isaias 59:1)." - Fr. Wathen


Of all the points that testify against a BOD, I think I like this one the best.

So let's examine the Johnsonian argument above.

Since Rahner's anonymous Christianity is even more extreme than the implicit BoD taught by some "Catholics", Feeneyites should no longer have any reason to oppos implicit BoD.  [Johnson is actually wrong in his analysis of Rahner, but I'll let the pass for now.]

I have no words for the epicness of this failure.

Pfeiffer:

In addition, it is found even before this millennium in the very early years of the Church without a single dissenting voice.

This abject lie alone completely discredits Pfeiffer.

Whatever Fr Pfeiffer, any other priest, the SSPX, any other group, any Father or Doctor of the Church ever taught on justification, as Catholics we are bound to stick to the Faith including the definitions and declarations of the extraordinary Magisterium of the Church:


Vatican I: SESSION 2 : 6 January 1870, Profession of faith

Profession of faith

1, I, Pius, bishop of the catholic church, with firm faith believe and profess each and every article contained in the profession of faith which the holy Roman church uses, namely:

[...]

6. I embrace and accept the whole and every part of what was defined and declared by the holy council of Trent concerning original sin and justification.

[...]

Trent:  SESSION 6 : 1547, Decree on Justification

DECREE ON JUSTIFICATION

Proem.

Whereas there is, at this time, not without the shipwreck of many souls, and grievous detriment to the unity of the Church, a certain erroneous doctrine disseminated touching Justification; the sacred and holy, oecuмenical and general Synod of Trent, lawfully assembled in the Holy Ghost,–the most reverend lords, Giammaria del Monte, bishop of Palaestrina, and Marcellus of the title of the Holy Cross in Jerusalem, priest, cardinals of the holy Roman Church, and legates apostolic a latere, presiding therein, in the name of our most holy father and lord in Christ, Paul III., by the providence of God, Pope,-purposes, unto the praise and glory of Almighty God, the tranquillising of the Church, and the salvation of souls, to expound to all the faithful of Christ the true and sound doctrine touching the said Justification; which (doctrine) the sun of justice, Christ Jesus, the author and finisher of our faith, taught, which the apostles transmitted, and which the Catholic Church, the Holy Ghost reminding her thereof, has always retained; most strictly forbidding that any henceforth presume to believe, preach, or teach, otherwise than as by this present decree is defined and declared.

[...]

CHAPTER VII.
 What the justification of the impious is, and what are the causes thereof.

[...]

Of this Justification the causes are these: the final cause indeed is the glory of God and of Jesus Christ, and life everlasting; while the efficient cause is a merciful God who washes and sanctifies gratuitously, signing, and anointing with the holy Spirit of promise, who is the pledge of our inheritance; but the meritorious cause is His most beloved only-begotten, our Lord Jesus Christ, who, when we were enemies, for the exceeding charity wherewith he loved us, merited Justification for us by His most holy Passion on the wood of the cross, and made satisfaction for us unto God the Father; the instrumental cause is the sacrament of baptism, which is the sacrament of faith, without which (faith) no man was ever justified; lastly, the alone formal cause is the justice of God, not that whereby He Himself is just, but that whereby He maketh us just, that, to wit, with which we being endowed by Him, are renewed in the spirit of our mind, and we are not only reputed, but are truly called, and are, just, receiving justice within us, each one according to his own measure, which the Holy Ghost distributes to every one as He wills, and according to each one’s proper disposition and co-operation.

[...]

Any teachings about justification without the sacrament of baptism are most strictly forbidden by the Vatican Council as well as by the Council of Trent. They are an attack on the true Faith as professed by the holy Roman Church.

So what are these "mysteries of the Faith which MUST necessarily be known and believed" that St. Pius X was referring to here?

Vatican I puts that nail in the coffin of Rewarder God theory by defining supernatural faith as something that has for its object a truth that can be known ONLY by Revelation.

So what are these "mysteries of the Faith which MUST necessarily be known and believed" that St. Pius X was referring to here?

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Given that the quote is actually from Benedict XIV, the answer would probably be found in his (rather than Pope St. Pius X's) corpus.  The footnote in the encyclical indicates a docuмent shorthanded as Instit. but I'm not sure what docuмent that is, and it could even be a private work of Pope Benedict's since he is largely regarded as one of the best theologian-popes and published many works aside from his pontificate.
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I know that in the context of Acerbo Nimis pope St. Pius X is considering primarily the poor state of education among Christians, and the paragraph where he cites Benedict XIV is one where he's just discussed how Christian faithful who had plenty of opportunities to learn, who were not weighed down by the obligations of their state, avoided all things religious and have tenuously left their religious instruction up to the priest who will be delivering them last rites.  So at least in that respect it is plain that the Pope isn't attempting to teach what articles of faith constitute the necessary elements for having supernatural faith, or even if any do.  It would be good, for these discussions, to see material which engages that point very directly rather than obliquely along the way to make a different point.