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How does that make anyone in the N.O. different from a Prot who thinks he is in the true Church?

Catholics who are not pertinacious heretics have the formal motive of faith, where they base their faith on the authority of the teaching Church, the Magisterium.  Protestants do not.  It has nothing to do with subjective sincerity.

Formal Motive refers not to WHAT I believe but WHY I believe it.

If I have the right WHY, i.e. because it's the Church teaching it, I am a Catholic, even if I am mistaken about the WHAT.  I think the Church teaches [this error], and so I believe it FOR THAT REASON.

Prots not only do not believe the right doctrines, but even the ones they DO believe, they believe for the wrong reasons, without the right rule of faith.

That is why the Church teaches that if you deny one dogma, you deny them all.  That's because you deny the authority behind ALL the dogmas, and whatever dogmas you still "believe", you don't believe them with the correct supernatural motive of faith but for your own reasons, making yourself (as St. Thomas points out) your own rule of faith.

In theory, you could have someone who believes every single dogma the Church has ever taught but simply have come to that conclusion due to their own reading of the Bible and their own interpretation.  Despite MATERIALLY believing everything, using the term "believe" loosely, since it's not supernatural faith at that point, they do not have the right FORMAL MOTIVE of faith, and therefore no faith.  No that this every happens in practice, but it's a hypothetical to illustrate the distinction.

It's the lack of such distinctions that causes many SVs to err, not distinguishing between the content of believe and the formal motive of faith, and failing to distinguish between the theological notes.

Catholics who are not pertinacious heretics have the formal motive of faith, where they base their faith on the authority of the teaching Church, the Magisterium.  Protestants do not.  It has nothing to do with subjective sincerity.

Formal Motive refers not to WHAT I believe but WHY I believe it.

If I have the right WHY, i.e. because it's the Church teaching it, I am a Catholic, even if I am mistaken about the WHAT.  I think the Church teaches [this error], and so I believe it FOR THAT REASON.

Prots not only do not believe the right doctrines, but even the ones they DO believe, they believe for the wrong reasons, without the right rule of faith.

That is why the Church teaches that if you deny one dogma, you deny them all.  That's because you deny the authority behind ALL the dogmas, and whatever dogmas you still "believe", you don't believe them with the correct supernatural motive of faith but for your own reasons, making yourself (as St. Thomas points out) your own rule of faith.

In theory, you could have someone who believes every single dogma the Church has ever taught but simply have come to that conclusion due to their own reading of the Bible and their own interpretation.  Despite MATERIALLY believing everything, using the term "believe" loosely, since it's not supernatural faith at that point, they do not have the right FORMAL MOTIVE of faith, and therefore no faith.  No that this every happens in practice, but it's a hypothetical to illustrate the distinction.

It's the lack of such distinctions that causes many SVs to err, not distinguishing between the content of believe and the formal motive of faith, and failing to distinguish between the theological notes.

To clarify, the content in this case being V2 and the motive still being faith? NO adherents are therefore still Catholic due to their motive even if the content is incorrect?

But that is the whole point of the poll. This forum is divided about if they have "legit authority" or not, and I am asking how it is possible that they do? The other polls demonstrate there is a MASSIVE disconnect in the brains of individuals who claim the N.O. is NOT The Catholic Church but a false religion, and one cannot belong to a false religion and still be Catholic, no heretics belong to the Church, etc. But then still somehow believe that the hierarchy of the N.O. is legit. They would like to use many distinctions, legalisms, specious arguments, subjective analysis, speculation, etc., to favor a paper-pope who is an "anti-Catholic heretic", but still true pope, and a College of Cardinals and local Ordinaries that are all onboard and always have been with the heresies of Vatican II (at least materially and in many cases formally). How can such a hierarchy be the true hierarchy of the Catholic Church? If you follow them - they will lead you to hell. R&R is trying to save face - the alternative is scary, and they shudder to think of the alternative - so they have to twist/wriggle to maintain the farce of having a more calming view of the situation and continue to perpetuate the false illusion that he N.O. is still somehow the Catholic Church.

maybe that's just it. Not recognizing and resisting IS scary. It's makes you into a pariah. The Latin Mass alone on Sunday doesn't make you a strong Catholic in any way shape or form. Ever notice how a lot of R&R's tend to be worldy for what they supposedly adhere to?