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In another place the soul describes the entry into Heaven of a woman who was not Catholic but who died making an act of perfect contrition, which was accepted by God.

In light of the dogma, which binds us to believing under pain of mortal sin that there is no salvation outside the Church, how is it that you are able to believe that a woman who was not Catholic, was able to even make an act of perfect contrition at all? -  and on that account, made it to heaven. To believe that both the story and the dogma are true, is ipso facto to deny that one of them, the dogma, is true. Which is to say that if the non-Catholic was saved, then the dogma is a lie.

The only way anyone can believe the story, is to disbelieve the dogma, which is a sin. It is impossible to believe that both the dogma and the story are both true. That is, it is impossible to believe the dogma that non-Catholics cannot be saved, while at the same time believe that a non-Catholic was saved without denying the dogma.

OK, we've got two of you on record.  Where's NO?  Laddy says that ABL was in "grave error."  And struth believes in dogma, not fallible men like ABL.  What a champion of the faith he is!
How about you, Matthew?  Do you take a similar position?  Are you in the camp of these two theological CI giants? Do you reject "fallible men" like the Archbishop, while declaring unyielding, unwavering allegiance to true "dogma?"  This is your blog.  You reprint everything that +Williamson writes, who, along with the other bishops I am certain, holds the erroneous views of ABL.  Where do you stand, sir? After all, you say this is a Resistance site, and +W is the putative leader of that Resistance.  How about it?

Yeah, we knew you were asking the question because you're trolling to get us banned ... to confirm you in your erroneous/heretical views.

So, what, then, nothingsworth, you DO consider Archbishop Lefebvre to have been infallible?

You R&R guys accuse the man whom you assert to be the Vicar of Christ to be guilty of grave error and even heresy, and that's OK?  But +Lefebvre is above the Magisterium somehow?

Cardinal Billot explains that some Protestants can be material heretics. "Heretics are divided into formal and material. Formal heretics are those to whom the authority of the Church is sufficiently known; while material heretics are those who, being in invincible ignorance of the Church herself, in good faith choose some other guiding rule. So the heresy of material heretics is not imputable as sin and indeed it is not necessarily incompatible with that supernatural faith which is the beginning and root of all justification. For they may explicitly believe the principal articles, and believe the others, though not explicitly, yet implicitly, through their disposition of mind and good will to adhere to whatever is sufficiently proposed to them as having been revealed by God. In fact they can still belong to the body of the Church by desire and fulfil the other conditions necessary for salvation. Nonetheless, as to their actual incorporation in the visible Church of Christ, which is our present subject, our thesis makes no distinction between formal and material heretics, understanding everything in accordance with the notion of material heresy just given, which indeed is the only true and genuine one. For, if you understand by the expression material heretic one who, while professing subjection to the Church's Magisterium in matters of faith, nevertheless still denies something defined by the Church because he did not know it was defined, or, by the same token, holds an opinion opposed to Catholic doctrine because he falsely thinks that the Church teaches it, it would be quite absurd to place material heretics outside the body of the true Church; but on this understanding the legitimate use of the expression would be entirely perverted. For a material sin is said to exist only when what belongs to the nature of the sin takes place materially, but without advertence or deliberate will. But the nature of heresy consists in withdrawal from the rule of the ecclesiastical Magisterium and this does not take place in the case mentioned [of someone who is resolved to believe all that the Church teaches but makes a mistake as to what her teaching consists in], since this is a simple error of fact concerning what the rule dictates. And therefore there is no scope for heresy, even materially."

Cardinal Billot says a Catholic who makes a mistake of fact is not in fact any kind of heretic - not even material, and this is important because canon law of old had some censures for those who are even material heretics. So, material heretics are non-Catholics. 

The question is, can someone who is a material heretic obtain the grace of final perseverance? The answer Fr. Mueller and other theologians give is, if he co-operates with the graces God gives him, God in His mercy will give him that grace, by enabling him to repent of his Protestant heresies before death. But He won't give final perseverance to someone who has not become a Catholic. 

Material heretics, per the explanation of Cardinal Billot, can be in the state of grace. But they will either be lost for other mortal sins and thus perish in them as Protestants, or if they co-operate with God Who wants them to be converted and saved, they will be converted.

Thus the statement of Pope Gregory XVI that "men are saved only in the Catholic religion" and that heretics do not attain eternal life.