St Thomas Summa Theologiae II-II, Q.5:

Article 3. Whether a man who disbelieves one article of faith, can have lifeless faith in the other articles?

Objection 1. It would seem that a heretic who disbelieves one article of faith, can have lifeless faith in the other articles. For the natural intellect of a heretic is not more able than that of a catholic. Now a catholic's intellect needs the aid of the gift of faith in order to believe any article whatever of faith. Therefore it seems that heretics cannot believe any articles of faith without the gift of lifeless faith.

Objection 2. Further, just as faith contains many articles, so does one science, viz. geometry, contain many conclusions. Now a man may possess the science of geometry as to some geometrical conclusions, and yet be ignorant of other conclusions. Therefore a man can believe some articles of faith without believing the others.

Objection 3. Further, just as man obeys God in believing the articles of faith, so does he also in keeping the commandments of the Law. Now a man can obey some commandments, and disobey others. Therefore he can believe some articles, and disbelieve others.

On the contrary, Just as mortal sin is contrary to charity, so is disbelief in one article of faith contrary to faith. Now charity does not remain in a man after one mortal sin. Therefore neither does faith, after a man disbelieves one article.

I answer that, Neither living nor lifeless faith remains in a heretic who disbelieves one article of faith.

The reason of this is that the species of every habit depends on the formal aspect of the object, without which the species of the habit cannot remain. Now the formal object of faith is the First Truth, as manifested in Holy Writ and the teaching of the Church, which proceeds from the First Truth. Consequently whoever does not adhere, as to an infallible and Divine rule, to the teaching of the Church, which proceeds from the First Truth manifested in Holy Writ, has not the habit of faith, but holds that which is of faith otherwise than by faith. Even so, it is evident that a man whose mind holds a conclusion without knowing how it is proved, has not scientific knowledge, but merely an opinion about it. Now it is manifest that he who adheres to the teaching of the Church, as to an infallible rule, assents to whatever the Church teaches; otherwise, if, of the things taught by the Church, he holds what he chooses to hold, and rejects what he chooses to reject, he no longer adheres to the teaching of the Church as to an infallible rule, but to his own will. Hence it is evident that a heretic who obstinately disbelieves one article of faith, is not prepared to follow the teaching of the Church in all things; but if he is not obstinate, he is no longer in heresy but only in error. Therefore it is clear that such a heretic with regard to one article has no faith in the other articles, but only a kind of opinion in accordance with his own will.

Reply to Objection 1. A heretic does not hold the other articles of faith, about which he does not err, in the same way as one of the faithful does, namely by adhering simply to the Divine Truth, because in order to do so, a man needs the help of the habit of faith; but he holds the things that are of faith, by his own will and judgment.

Reply to Objection 2. The various conclusions of a science have their respective means of demonstration, one of which may be known without another, so that we may know some conclusions of a science without knowing the others. On the other hand faith adheres to all the articles of faith by reason of one mean, viz. on account of the First Truth proposed to us in Scriptures, according to the teaching of the Church who has the right understanding of them. Hence whoever abandons this mean is altogether lacking in faith.

Reply to Objection 3. The various precepts of the Law may be referred either to their respective proximate motives, and thus one can be kept without another; or to their primary motive, which is perfect obedience to God, in which a man fails whenever he breaks one commandment, according to James 2:10: "Whosoever shall . . . offend in one point is become guilty of all."

Never mind Baptism of Desire for the moment.  The above question deals with whether anyone who doesn't assent to the doctrines of the Church (regardless of whether they are validly baptized or not) can be said to have divine faith (which St Thomas teaches is necessary for salvation).  The answer is no!  Only those who profess the Catholic faith have divine faith.  All others do not have the motive of faith.  We affirm this whenever we make a traditional act of faith.  e.g. "O my God, I firmly believe that Thou art one God in three divine persons, Father, Son and Holy Ghost; I believe that Thy divine Son became man and died for our sins, and that He shall come to judge the living and the dead. I believe these and all the truths which the holy Catholic Church teaches, because Thou hast revealed them, Who canst neither deceive nor be deceived. Amen."

So even those validly baptized Protestants who are not guilty of the sin of heresy (because they are invincibly ignorant of the Catholic faith) do not have the divine faith which is necessary for their salvation.  It is true that some theologians say that only explicit belief in the Holy Trinity and the Incarnation are necessary and that is true but the motive of faith is also necessary.  The person in question may only explicitly know and believe in the doctrines of the Holy Trinity and the Incarnation but they must also have the belief that all that the Catholic Church teaches is from God and must be believed.  Without that motive of faith, the person does not possess any faith at all.   All of the preceding only applies to those who have the use of reason.  Those who do not have the use of reason need only be validly baptized.

Now this doctrine of St Thomas completely obliterates the modernist teaching that Jєωs, Mohammadens and pagans as well as Protestants can be saved by their sincerity in seeking God and their adherence to natural law.  Regardless of what you believe concerning BOD of catechumens, it has been the universal teaching of the magisterium as well as Catholic theologians (at least until the mid 19th century) that non-Catholics cannot be saved.  St Thomas says it is necessary for salvation for each individual to PROFESS the Catholic faith.  Merely having a longing for entrance into the Church is NOT enough.  It is absolutely necessary to have the motive of faith and to profess it publicly.  The remedy for Original Sin (disbelief in the commandments of God) is belief in all that God has revealed through the Catholic Church.  Which includes the doctrine that the Sacrament of Baptism is necessary for salvation.

They have the natural virtue of faith, but the supernatural virtue if faith they do not.

The simplest proof of this is their distrust of any religious authority outside of themselves. If they had supernatural faith they would take Our Lord at His word when He established His Church on St. Peter, simultaneously creating an order of clergy as well as introducing sacramental theology.

Great thread.  I have been arguing this point for years but have been largely ignored.

This is the key to understanding what is really meant by “formal” heresy ... a term that has deliberately been watered down into a question of “sincerity”.

Great thread.  I have been arguing this point for years but have been largely ignored.

This is the key to understanding what is really meant by “formal” heresy ... a term that has deliberately been watered down into a question of “sincerity”.

//Hence it is evident that a heretic who OBSTINATELY disbelieves one article of faith, is not prepared to follow the teaching of the Church in all things; but if he is not obstinate, he is no longer in heresy but only in error. Therefore it is clear that such a heretic with regard to one article has no faith in the other articles, but only a kind of opinion in accordance with his own will.//

I think saying it just means sincerity is a strawman of people who agree with Lefebvre, and it wrongly maligns them with the more liberal theology of guys like Barron.

Lefebvre of course believed that perfect contrition was necessary for any visible non Catholic to be saved, and presumably, perfect contrition wouldn't really exist at the same time as obstinancy.

if Aquinas really meant what Feeneyites think he means, what's the point of the obstinancy criterion?

Did you know that some Protestants say they're NOT Protestant; they're "Christians"?  Hoo boy.  My Mother-in-law is one such.  

Here's something:  My 7 year old son went up to his grandma yesterday -- who was surrounded by the other 10 of my children -- and said, "Grandma, why don't Protestants say after meal prayers?"  You could have heard a pin drop...she just sighed quite loudly in irritation and closed her eyes.  

You can't talk to some of these people.  They don't have the true Faith, and they don't want it.  

Ah yes non denominationals. I once had a guy tell me that they are the worst people to talk to about theology after muslims. This one non denom in this chatroom claims he doesn't sin and talking to him was very frustrating. He claimed sola scriptura was "common sense."

XavierSem ... total falsification of St. Thomas.  He says the opposite of what you falsely attribute to him.  It is not required to commit mortal sin against the faith to not have faith.  St. Thomas teaches that those who lack faith out of invincible ignorance, while not sinning against faith, are not given the grace of faith due to other sins and various other obstacles to God’s grace.  Faith can be lacking without an actual sin against faith.

So please stop lying.

But Invincible Ignorance is unanimously taught by all theologians in the Manuals.

Invincible ignorance is merely exculpatory and cannot supply for lack of faith ... again, as clearly taught by St. Thomas.  This has nothing to do with the requirements for supernatural faith.

Your attempt to equate exculpation of sin against faith with the actual possession of faith is Pelagian.

So even those validly baptized Protestants who are not guilty of the sin of heresy (because they are invincibly ignorant of the Catholic faith)

How can you guys argue that a baptized person is invincibly ignorant of the Church?  That’s a denial of 1) the supernatural effects of baptism, which infuses faith, hope, and charity, and 2) a denial of the effects of sanctifying grace, and of the enlightenment of the Holy Ghost.  
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A baptized person is a member of the church, and thus, they are not invincibly ignorant of Her.  To say the opposite makes no sense.