This is a bad comparison you are making (due to the nature of manifest, public heresy), see:
https://www.cathinfo.com/crisis-in-the-church/'popes'-of-the-western-schism-same-as-the-'popes'-of-vatican-ii/

This is obviously the context St. Vincent meant the following in (a formal adherence to an antipope when known);

“...by adhering to one who is not pope, as though he were pope, by showing papal reverence to him, they transgress the first precept of the first table, in which is commanded to man: ‘thou shalt not worship a strange god, nor idols, nor a statue, nor any likeness from heaven.’ For who indeed is a false pope, if not some strange god in this world, or an idol, or a statue, or the fictitious likeness of Jesus Christ?”

-St Vincent Ferrer

But the Saint didn't have a problem with people thinking Pope A was real while going to a Mass where the priest thought Pope B was real. This means that those who assist are NOT showing papal reverence to the specifically named pope the priest is mentioning in the canon.

Again, you are missing the critical distinction that those times (Western Schism) what divided them was not issues of doctrine/heresies as it is now between trads and the conciliar church.

The nature of the crisis then was different, those people only had material errors about who was Pope, but among all the potential "Popes" they were all orthodox, not like now when all the post-vatican II claimants are manifest public heretics that push their heresy to all.

I was addressing what you gave St. Vincent to say, "adhering to one who is not pope, as though he were pope, by showing papal reverence to him". What I said fits that.

Sure, but using the Western Schism as a comparison is bad it "doesn't fit" our current crisis due to the nature of manifest, public heresy.

It only addresses the FACET of the "lie". As if a lay person who believes Pope A is legitimate and assists at a Mass where the priest believes Pope B is legitimate would be lying. The fact that St. Vincent had no problem with that shows it is not a lie.

Of course the right distinctions have to be in place, thus if one is not truly convicted of the manifest public heresy of these pretenders they would not be sinning in the subjective sense by ignoring their Catholic-formed conscience - only God can read the heart.

Which is to say that sedes believe faithful trads who live according to the faith but without concerning themselves of the status of popes, probably sin, and on that account sedes believe that "not only is it allowed but it would be OBLIGATORY to separate from their communion."  Which is to say not being concerned with a heretical pope's status either can be or is a sin. 

Well, if that's the reason, that's a ridiculous reason. 

I am culling a principle

The point being, it was not strictly considered a profession of a particular man. It was merely implied that you wanted to be in union with the pope, whomever he is. The profession is the formal intention.

Agreed.

But, it is still a bad example, to use compared to now.

During these times one must decide if they believe the papal claimants since Vatican II are just bad dad Popes who are really really naughty and sin 'o' bunch, downplaying or flat out denying papal infallibility, and the necessary unity in faith among members.

Or, they are convicted with moral certitude that the men who claim to be Pope are actually quite manifestly and publicly heretical and therefore are the head of nothing and as a result hold no communion with true Catholics (and those same Catholics openly declare that they have no communion with the pretenders either).

If I have moral certitude that something done is an evil, I cannot participate in it without implicating myself in the crime, because I would be acting against my conscience. Now, maybe the thing I thought was an evil is actually no evil at all, but it would be a sin to against against the moral certainty I was convicted of.

According to the teaching of St. Thomas, If you have knowledge of the priest's unrepented lifestyle ( even other-less-serious sins compared to heresy - such as having a mistress) you cannot participate at his Masses without sin.

For sedes who have moral certitude about the manifest heresy of the post-conciliar claimants it is the same principle.

It is great that everyone agrees that having the formal intention to be united to the papacy as one in faith and subordination to legitimate authority is 100% Catholic.

we all agree that no one during the Western Schism concerned themselves with the debate simply because heresy was a non-issue.

Yet, It would be false to omit the critical distinction that when one has moral certitude that an evil is being  committed that they are free to join themselves to those acts without sinning, and in this case, that evil would be to name a manifest, public, heretic as being one in eccelsisial faith and subordination before God, which would be to give public credence to what you believe is lie and it would be to scandalize all those who do not understand that a manifest, heretic cannot be Pope.

Again, the crucial distinction is, does one have this moral certitude or not?

Maybe some people don't have it because they haven't studied the issues,
maybe some people don't have it because they disagree,
maybe some people don't have it because they have something to lose,
maybe...etc.

If you have this moral certitude, you must follow your Catholic conscience.
If you don't, you must follow your Catholic conscience.

But, this is why it is an issue for some. It is based on Catholic principles. It is no mad thing to think twice before saying to God during the Holy Sacrifice that you are in communion with heretics and subordinate to them. It is very Catholic indeed to pause and do some searching on that. 

All I am doing is saying what it means, and doesn't mean, at the very moment when you are assisting at a Mass and the priest mentions a pope in the canon.

It does NOT entail that you yourself are MEANING and SAYING the pope's name. You have to come to grips with that. That is the only purpose I mentioned the historical account surrounding St. Vincent. If people actually believed they were also saying the name of the pope with the priest, it would have been a BIG historical deal. But it was absent in the circuмstances, and absent afterward for theologians to look back on.

If you are morally certain that the one so named in the Canon is a manifest, public heretic - you are not allowed to ignore you convictions (if you even have them).

The meaning of the prayer is clear, recent arguments have tried to distort the historical reality of what the prayer signifies so as to downplay the nature of manifest, public heresy. 

It signifies being one in faith and subordination to legitimate authority.

When you attend Mass you attend that priest's Mass - he is standing in for you and you unite yourself with him. So, again if you know he is living as an unrepentant public sinner, or in our case you are morally certain he is a manifest, public heretic, you cannot attend his Masses without sin. 

Equally, if you are morally certain that the one named as the head of the Church is a manifest, public heretics and therefore not a Catholic or the head of the Church you cannot ignore these truths if you have that conviction - to do so would be to agree to a lie before God about what faith is, who has it, what faith you have/want, and the unity and subordination that it requires towards legitimate authority. 

For some sedes they are morally certain they that the SPECIFIC man who happens to be sitting in the Chair of St. Peter at this time (Bobby Prevost) is a manifest, public heretic, therefore this moral certainty necessitates action for them. It is not a novelty to think thus, but is rather based on history, the meaning of the liturgy, and Catholic moral principles. 

To remove the name of a manifest, public heretic from the Canon - is the historically Catholic thing to do (as this thread details).
https://www.cathinfo.com/the-sacred-catholic-liturgy-chant-prayers/una-cuм-question-an-ai-bug-or-catholic-teaching/

If one is not truly convicted that the post-conciliar claimants are indeed manifest, public heretics, then that is where the R&R "resistance" to this often comes into play. 
Simply because they lack this certainty and do not want to be told that they need to have it as a matter of faith. 

Further it would be incorrect to tell them it is a matter of faith without first establishing the principles one is discussing. 

I think all R&R agree that the Canon signifies communion in faith and subordination with the legitimate authority. 
Where they disagree is, for them - the matter of the manifest, public heresy of the Vatican II Popes - is simply a private opinion and therefore no judgments should enter into the public acts of worship. 

Normally they would be right, but there is an important moral principle they are overlooking, that of following a morally certain conviction. It is the same principles +Lefebrve used to defend himself against the excommunication. He though the priesthood/faith was threatened. He was moral certain it, He was convicted, He HAD TO ACT.

This is all validated by the historical example of Nestorius' name being removed from the sacred mysteries before an official judgement was ratified by the Pope. The bishops and priests argued about it back and forth for a year or more before Ephesus settled the matter.

NO CHANCE OF DELETING OR EDITING THE PREVIOUS ATTEMPT TO POST THIS, so here it is again:

SkidRow, Please change your use of the term "convicted" to "convinced" or else you are liable to be misunderstood by others.

I am FULLY behind sedevacantist NOT attending R&R Masses for extrinsic reasons. But theoretically, there is nothing intrinsically wrong with assisting at the moment of the canon where the name of the pope occurs.

Look at the common denominator:

“As for the one who, during a time of schism, mentions in the Canon the name of him whom he believes to be the true Pontiff, even if he should be mistaken, he does not sin, provided he does so out of reverence for the office and from a desire to maintain ecclesiastical unity. For he intends to name the Supreme Pontiff, and the Sacrifice is offered for the whole Church, under whomever Christ has placed as its head.”

— St. Robert Bellarmine, De Controversiis, Tom. II, De Conciliis, Lib. II, Cap. 19


“During the time of the Great Schism, priests were often bound by obedience to their lawful superiors to mention a particular name in the Canon. If they did so in good faith, following the directions of their bishop or the recognized authority in their region, they did not incur sin or render the Sacrifice invalid—even if the one named was not, in fact, the true Pontiff. For the intention of the priest is to offer the Sacrifice in union with the Catholic Church and its visible head, whom he honestly, though perhaps erroneously, believes to be such.”

— St. Antoninus, Summa Theologica, Pars III, Tit. 23, Cap. 4, § 6


“In the perplexity of a schism, the priest who, following the counsel of his ordinary or the common estimation of learned men, commemorates in the Mass that claimant whom he considers legitimate, commits no fault, nor does he violate the due order of the Sacrifice. The essence of the commemoration is not adherence to a person, but to the See and the unity it represents.”

— Francisco Suárez, S.J., De Sacramentis, Disp. 83, Sect. 3


“In the case of a doubtful pope, it is the common teaching that a priest who, guided by probability and the counsel of prudent men, commemorates one of the contenders in the Canon, does not sin. For he does not intend to separate himself from the unity of the Church, but rather to adhere to it according to his best judgment. The Mass is offered for the universal Church, and the commemoration is made of him who is presumed to be its head.”

— Cardinal Juan de Lugo, S.J., De Virtute Fidei Divinae, Disputatio 16, Sectio 4


“In the time of schism, those who in good faith adhere to one of the contenders for the Pontificate, and during the Holy Sacrifice name him in the Canon whom they believe to be the legitimate successor of Peter, are not to be considered as acting against unity; rather, they intend to profess that unity by rendering due obedience to him whom they judge to be the head of the Church on earth. The merit of this act is founded upon their intention to maintain Catholic communion.”

— St. Alphonsus Liguori, Theologia Moralis, Lib. VI, Tract. 2, Cap. 1, Dubium 3


“It is a sound theological conclusion that during a papal schism, a priest who, in the Canon of the Mass, commemorates the man he in good conscience and with probable reason believes to be the true Pontiff, offers a valid and licit Sacrifice. The essence of the prayer is the unity of the Church under the successor of Peter, not the personal worthiness or even the certain legitimacy of the individual named. The error, if there is one, is one of fact, not of intention against the faith or the Church.”

— Ludovico Molina, S.J., Commentaria in Primam Partem Divi Thomae, Qu. 83, Art. 3