BOD is *not* de fide
To the contrary, St.Alphonsus indeed affirms, "it is
de Fide that men are also saved by Baptism of desire"
so therefore we are free to *not* believe it.
Well, even if the premise was true, this conclusion would not follow. All are agreed baptism of desire is at least proximate to the Faith, so the following would apply.
(d) Theological Note: Proximate to faith.
Explanation: A doctrine all but unanimously held as revealed by God.
Example: Christ possessed the Beatific Vision throughout his life on earth.
Censure attached to contradictory proposition: Proximate to error.
Effects of denial: Mortal sin indirectly against faith.
Source "On the Value of Theological Notes and the Criteria for Discerning Them by Father Sixtus Cartechini S.J. (Rome, 1951)"
So it is a mortal sin, objectively speaking. Ignorance, of course, may excuse if it was inculpable.
The precise error is that it is we who are bound by the Sacrament, not God, yet BOD proponents judge that God grants salvation without it based on teachings of learned fathers of the Church - but it is not the universal and constant teaching and, IMO, not only can be wrong but needs to have many important contradictions answered.
Well, St.Thomas in explaining the doctrine has already, as he is wont to do, mostly dismantled almost all objections that can be offered against this doctrine. It has also been explained in some depth by the Holy Office under Cardinal Ottaviani along with the express approval of Pope Pius XII.
Now, even if you don't accept the authority of this letter, at least reading it may help you understand implicit desire for baptism better. From the questions you ask, it seems you may not have read or at least fully remembered what it said. Correct me if I am wrong. Here are some excerpts.
Now, among those things which the Church has always preached and will never cease to preach is contained also that infallible statement by which we are taught that there is no salvation outside the Church.
However, this dogma must be understood in that sense in which the Church herself understands it. For, it was not to private judgments that Our Savior gave for explanation those things that are contained in the deposit of faith, but to the teaching authority of the Church.
...
However, this desire need not always be explicit, as it is in catechumens; but when a person is involved in invincible ignorance God accepts also an implicit desire, so called because it is included in that good disposition of soul whereby a person wishes his will to be conformed to the will of God.
But it must not be thought that any kind of desire of entering the Church suffices that one may be saved. It is necessary that the desire by which one is related to the Church be animated by perfect charity. Nor can an implicit desire produce its effect, unless a person has supernatural faith: “For he who comes to God must believe that God exists and is a rewarder of those who seek Him” (Heb. 11:6).
Because God is Almighty, no one who sincerely desires baptism will be denied it - this is the way the Divine Providence works. That is what the universal and constant teaching of the Church is on the doctrine of Divine Providence.
Certainly, but extraordinary means of the sacraments themselves are examples of Divine Providence in action par excellence. The matter or water is only a poor creation of God, the minister as well only a poor instrument, both can be utterly dispensed with, if God in His supreme wisdom so decides, by the sanctifying action of His Spirit alone without these ordinary means in extraordinary circuмstances.
The Doctors of the Church, and the Church herself, tell us that He so decides. Therefore, we must regard the matter as settled.
The constant and universal - and also infallibly defined and declared teaching of the Church is that the Sacrament of Baptism is necessary for salvation.
Which must be understood as the Church herself understands it, and as it has always been understood, as St.Thomas explains
"The sacrament of Baptism is said to be necessary for salvation in so far as man cannot be saved without, at least, Baptism of desire; "which, with God, counts for the deed. (Augustine, Enarr. in Ps. 57)" [St. Thomas Aquinas, Summa Theologica, Whether a man can be saved without Baptism?]
As to your question, I think Pope Pius XII's Encyclical Letter as well as the Holy Office's authoritative clarification should suffice. Again,
"an implicit desire [is] so called because it is included in that good disposition of soul whereby a person wishes his will to be conformed to the will of God ... It is necessary that the desire by which one is related to the Church be animated by perfect charity." etc
Finally, the letter sounds a warning,
Therefore, let them who in grave peril are ranged against the Church seriously bear in mind that after “Rome has spoken” they cannot be excused even by reasons of good faith. Certainly, their bond and duty of obedience toward the Church is much graver than that of those who as yet are related to the Church “only by an unconscious desire.”
Let them realize that they are children of the Church, lovingly nourished by her with the milk of doctrine and the sacraments, and hence, having heard the clear voice of their Mother, they cannot be excused from culpable ignorance, and therefore to them apply without any restriction that principle: submission to the Catholic Church and to the Sovereign Pontiff is required as necessary for salvation.