Faith of the Fathers?
But though the doctrine which men hold be false and perverse, if they do not maintain it with passionate obstinacy, especially when they have not devised it by the rashness of their own presumption, but have accepted it from parents who had been misguided and had fallen into error, and if they are with anxiety seeking the truth, and are prepared to be set right when they have found it, such men are not to be counted heretics. Were it not that I believe you to be such, perhaps I would not write to you
Both these quotes refer to explicit BoD
The proposition that theologians, authorities, Saints and Doctors (especially after Innocent II and III) teach pertains to Catholic doctrine is "there are souls that have been saved by baptism of desire".
This is the truth that you need to confess under pain of mortal sin.
Fr. Cekada also provides extensive docuмentation that at least after these medieval pronouncements of the Magisterium, all theologians ascribe to the proposition above a grade of certitude so high that it cannot be called into question without mortal sin.
these are non-infallible teachings
Pius XII answers this liberal excuse thus, "Nor must it be thought that what is expounded in Encyclical Letters does not of itself demand consent, since in writing such Letters the Popes do not exercise the supreme power of their Teaching Authority. For these matters are taught with the ordinary teaching authority, of which it is true to say: "He who hears you, hears me"; and generally what is expounded and inculcated in Encyclical Letters already for other reasons appertains to Catholic doctrine. But if the Supreme Pontiffs in their official docuмents purposely pass judgment on a matter up to that time under dispute, it is obvious that that matter, according to the mind and will of the Pontiffs, cannot be any longer considered a question open to discussion among theologians"
These medieval teachings of the Holy See are authoritative and binding (those of Innocent II and Innocent III are included in Denzinger nos. 388 and 413), as the subsequent consensus among theologians also shows.
"unbaptized priest"
The reference to the "priest who died without the water of baptism" is thought by some to refer to someone who, by an unfortunate mistake, was baptized invalidly in the medieval Church. Such a person would not have then been able to receive any of the other sacraments. When the mistake was discovered, the question arose. But the Pope (St. Cyprian had earlier said God is able to provide for such persons) responded with the calm assurance that this person is not deprived of the fruits of the sacrament, showing the mind of the Church on this matter.
Innocent II is relying upon Augustine
Peter has spoken through Innocent II, approving the teaching that binds us Catholics. He clearly disagrees with you that St. Ambrose is "ambiguous" and even if St. Augustine changed his opinion (which some scholars deny), the teaching the Magisterium makes its own is what henceforth concerns us.
EXPLICIT BAPTISM OF DESIRE
I already told you that you Feeneyites horribly confuse the issue, and this time I think it is deliberate on your part. The only matter discussed by the Doctors and theologians before Vatican II was not at all about baptism of desire but rather about explicit/implicit faith in Christ in those who receive the sacramental effect by this extraordinary means. That is the only topic that the Doctors and others considered an open question and that therefore can be discussed by Catholics, maybe I'll start a thread on that. I believe everything the Doctors believed on this subject, if you think otherwise, quote them against something I have said.
The Dimond link is so absurd it hardly merits a response - one example of their "reasoning" is like this: we know by our private judgment that Pope Innocent III's authoritative teaching is incorrect in other respects (like they imagine on circuмcision and original sin), therefore we use that same private judgment to reject this teaching of his as well. Classic liberals.