"Outside the Church there is no salvation" actually means that everyone is saved except for those who believe that outside the Church there is no salvation.

Right, any knowledge of truth just sets people up to be damned.

If I skip Mass on a Sunday then die on Monday, then I lose my soul.  But a Prot who shows up every couple months when the fancy suits him, he's fine.

With the new soteriology, the more we tell people, the better the chance that they'll be damned.

Dimondism is a formally condemned sect. To the extent a person knowingly adheres to it, he separates himself from the Catholic Church. Especially if he is a Dimondite Ecclesia-Vacantist, who professes that there is no Magisterium in the Church today, he is in as bad or a worse state than the average Protestant is. 

Now you're tipping your hand.  On the one hand you call Protestants "real Christians" but those who, while professing the Catholic faith and recognizing the Church as their rule of faith, perhaps (arguably) make some erroneous theological conclusions based on a profound crisis in the Church, these are as bad if not worse off than Protestants?  Those "Dimondite" Catholics have all the essentials of the Catholic faith and are left spinning in the Magisterial vacuum that is Bergoglio, left to make their own judgments, and may have made errors in some of their syllogisms.

This is shameful.

I've never met the Diamonds, or talked to them, or emailed them.  I've read some of their articles...that's it.  I've read more of your views, than theirs.
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You reduce anyone who disagrees with you to being a Diamondite.  That's so intellectually dishonest and lazy.

No, he knows better.  He tosses that word out there every time he gets frustrated.  I've corrected him a dozen times that many/most of us do not completely agree with the Dimonds on a number of issues.  So, for instance, I disagree with them that BoD is heresy and consider their characterization of anyone who believes in BoD as a heretic per se to entail a schismatic attitude.  I've been raked over the coals in e-mail by the Dimonds for being a heretic, and yet that never stops Xavier from periodically calling me a Dimondite.  If anything, I'm closer to a Feeneyite (with some nuances).

Dimondism is a formally condemned sect. 

Says who? I seem to have missed the formal declaration.

No they can’t.  That is the entire point made by St. Thomas in the OP.  Protestants lack the proper rule of faith and therefore lack the formal motive of faith.  Whatever doctrine they hold that happens to be true is materially correct but lacking the formal motive and therefore not supernatural faith. THAT is what formal vs. material means in the context of faith and NOT sincerity of belief.  You’ve been promoting this Pelagian nonsense for some time now.  Prot heresy is by definition FORMAL due to lacking the FORMAL motive.

I don't think the lack of the formal motive of faith necessarily makes you a formal heretic.  That might be an area of discussion.  Fr Michael Mueller would agree with St Thomas that heretics do not possess divine faith.  But on the other hand he says that there is a distinction between a material heretic and a formal heretic.  So if there is a distinction AND it is not possible for anyone outside the visible communion of the Catholic Church to have the formal motive of faith then it follows that not all those who lack the formal motive of faith are formal heretics.  I think the point is that not a single person who is outside the visible communion of the Catholic Church believes all that the Catholic Church (i.e. the one Church which God Himself, Jesus Christ, has founded) teaches because He has revealed it.  It is not possible because God can neither deceive nor be deceived.  If you asserted that it were possible to believe that the Lutheran Church was the true Church (because God revealed it, i.e. supernatural faith) then you would be asserting that God could deceive someone into believing it.  But that's not possible.  So they believe the Lutheran Church is the true Church for some other reason than that God revealed it.  Most likely because they trust in men or desire the approval of men rather than trust in God and desire the approval of God.  And so because of that, they are easily deceived by men into thinking that the Lutheran Church is the true Church of Christ.  If they truly seek the will of God, they will find their way to the Catholic Church.  That is St Thomas' position and if you examine the materials of Most Holy Family Monastery, you will see that they say the same thing.  Everyone who seeks God sincerely, will invariably come to know the Catholic Church.  And if they persevere, they will be granted the grace to enter the Church via the Sacrament of Baptism if they have not already received it.

I should also point out that a Catholic is never a material heretic.  I know it is popular nowadays to say that some Catholics are material heretics but where do theologians teach that?  I've not seen it.  Catholics may be in error about certain doctrines but as long as they have the formal motive of faith, they are not heretics, neither material nor formal.  The only question would be what evidence would be necessary to conclude that a Catholic who is obviously in error has lost the formal motive of faith?  For a cleric, it might be possible to say that any contradiction of dogma is sufficient evidence.  Or maybe some allowance must be made for the universal confusion of our times?  I'm not sure.  But certainly, if a guy claiming to be the Bishop of Rome says, "this might be heresy..." then you can be certain that he is a formal heretic.  Or if a peritus of a supposed ecuмenical council says with obvious pride that the council was the "French ʀɛʋօʟutιօn in the Church" then we can be certain he is a formal heretic.  The higher up in the hierarchy you go, the less evidence you need to prove formal heresy.  But what about an Archbishop who directly word for word contradicts a dogma of the Church and who shows that he is aware of the dogma but who gives clear signs that he is contradicting it because he believes that it is the Church Herself who contradicts it?  Can that be chalked up to confusion or do we have to conclude that he is a formal heretic?  I don't know.  I would like to give everyone the benefit of the doubt.  We are living in extraordinary times and confusion is universal.

I don't think the lack of the formal motive of faith necessarily makes you a formal heretic.  That might be an area of discussion.  Fr Michael Mueller would agree with St Thomas that heretics do not possess divine faith.  But on the other hand he says that there is a distinction between a material heretic and a formal heretic.  So if there is a distinction AND it is not possible for anyone outside the visible communion of the Catholic Church to have the formal motive of faith then it follows that not all those who lack the formal motive of faith are formal heretics.
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I should also point out that a Catholic is never a material heretic.  I know it is popular nowadays to say that some Catholics are material heretics but where do theologians teach that?  I've not seen it.  Catholics may be in error about certain doctrines but as long as they have the formal motive of faith, they are not heretics, neither material nor formal.

These are both somewhat slippery terms and are variously defined by many theologians.  I've seen a discussion somewhere by a more recent (pre-V2) theologian speaking about various definitions held by different theologians.

Yes, there are those who say Catholics cannot be formal heretics, due to the etymology of heresy (which entails pertinacity).  Others use it.  I like the term because it means that the Catholics are in material error about a matter that is dogmatic, i.e., where it would be "heresy" in the strict etymological sense to reject the truth.  So material heresy, in that sense, means material error about a matter that would contradict a dogmatic truth ... to distinguish it from being in material error regarding a truth of a lesser theological note.  I think that the disagreement there would be semantic ... except for ...

This is how they shifted the notion of material heresy into people who are heretics "in good faith" or "with sincerity".

I agree that not everyone who lacks the formal motive of faith is a formal heretic.  There are people to whom the term heresy doesn't even apply because they're infidels.  This term "formal heresy" specifically refers to those who are NOT infidels (in that they believe materially in the core truths of the Holy Trinity and Incarnation) but who do not hold these truths with the formal motive of faith, i.e. at least implicitly reject the formal motive behind all dogma.  So, for instance, take an Old Catholic, who might believe most dogmas but then rejects papal infallibility.  Since this teaching was delivered through the authority that underlies all dogmas, the rejection of this single dogma entails a rejection of the rule behind them all, replacing the correct formal motive of faith with a false one.

Where the issues started is with equating "formal" with "sincerity."  I am a well-meaning Protestant who sincerely believes my errors, so I am only a material heretic (as per Xavier's position).  Heck, who IS a "formal" heretic then?  I am sure that most Old Catholics and Protestants are convinced that they're right.  This limits formal heresy to those guys who are like, "Yeah, I know what the Church teaches, and I recognize that the Church teaches infallibly, but I don't like that particular dogma, so I refuse to accept it."  It's similar to the issue of saying that those who KNOW the Church to be the True Church but REFUSE to enter it anyway.  That would effectively render the term "formal heresy" meaningless, a matter only of the internal forum where God alone can judge TRUE sincerity or insincerity.  It leads to invisible Church (internal forum) ecclesiology.  It leads to all the errors we've been discussing here.

So, by formal heresy, I mean heretics who at least implicitly reject the rule of faith (the Church's teaching authority), and material heretics as Catholics who adhere formally to the rule of faith (acknowledge the Church's authority) but are mistaken about WHAT the Church teaches on a matter that would have the theological note of dogma.

Material heresy is only possible among someone who formally has the Catholic faith.  So, a Catholic who holds a heresy unaware that it was condemned by the Church. As soon as the person is told, “that’s condemned as heresy by the Church,” he immediately rejects it for that reason alone, having the true formal motive.  That’s what St. Augustine defines as the litmus test for material heresy.

I have a hard time believing this is the doctrine of St. Augustine.  Heresy, by definition, means a separation from the Church.  But a Catholic who makes a theological error is still a member of the Church.  So no heresy at all there.  It's only when a Catholic intentionally rejects a teaching of the Church that he becomes a heretic and in that case he is always a formal heretic.  The material/formal distinction is just to distinguish non-Catholics who are not guilty of intentionally rejecting a doctrine of the Church.  I don't think there are many material heretics.  In fact, I think they are likely to be exceedingly rare.

This definition includes every single Protestant.  And in fact it's practically THE definition of Protestantism.  They claim that they believe in the Gospel, but they pick and choose how to interpret it, setting themselves up as the ultimate RULE of faith, and rule of interpretation, rather than having the infallible rule of faith in the Church's teaching that is required for supernatural faith.

You just destroyed your entire position with this quote.

Yes, true.  But as you mentioned already, it is possible for Protestants (maybe young children) to have not gotten to the point of choosing what to believe.  They just believe whatever they are told and make no effort to think for themselves.  That is what we would call a material heretic.  But they are exceedingly rare.  Once they get to the point where they are ready to start choosing what to believe, they would need to choose to believe whatever God has revealed.  But for Protestants that almost never happens.  They are trained from a young age to just believe in Jesus and then they can do whatever else they want as long as it doesn't make their parents angry.  That's not even close to having the formal motive of faith.  And we see that the Novus Ordo is very similar.  Even the conservatives.  Why are they conservative?  Because it appealed to their sensibilities?  That's not the formal motive of faith.  We have to be able to make the traditional Catholic Act of Faith in truth.  Obviously, all of us have an admixture of motives.  But the overriding motive has to be the same as the Act of Faith.