Snip from Who Shall Ascend? by Fr. Wathen:

"....The divisive aberration of Sedevacantism is due to nothing else than certain priests' losing sight of their proper roles in our present malaise. To save the Church from an heretical pope was never their assignment. Securing the  Apostolic succession of the Church was  never their assignment. What was their assignment? It was to take care of the people whom God sent them as best they could, say their prayers faithfully, study and pray that they might not themselves fall victim to the spirit of Liberalism and worldliness, and keep their torment and speculations to  themselves. The hierarchical structure of the Church and the papacy are not their business. Such high matters are the province of none other than Christ Himself and His Mother and the Apostles.

[...]

[Tell your priest or bishop respectfully]....I can see that it is not necessary for you or for me  to know whether Pope John Paul is the legitimate successor of St. Peter. It doesn't hurt anything to pray for him in the Mass; it surely could not be wrong to do so, even if it is an honest mistake. Pope or not, God knows that he who is called John Paul II needs our prayers, as all of us need God's mercy. But to attack the office of the papacy, and to separate oneself from it, is a serious thing to be wrong about. This Sedevacantism is your opinion. But the Mass not yours, and I know you do not have the right to change a word of it. I have heard you say the same thing about those who brought in the New Mass. And now this is what you have done!..."

John Daly notes that it is comparable to the English putting the name of the King (an Anglican heretic) in the Te Igitur.
https://tradcath.proboards.com/thread/2154/response-una-controversy-daly-2006

I think that's wrong ... especially after Pope St. Pius V's deposition of Elizabeth I, which illegitimizes the entire line.  Nor should any open/professed/condemned heretic be included in the Canon.  There's a tendency among many SVs in particular to claim that anything that happened prior to 1959 was OK and permissible.  Negatory.  Modernism was well advanced by then, and religious indifferentism was well underway by the time of Pope Pius IX.  There has been a massive decay of faith since Pope St. Pius V even.

But putting these V2 papal claimants into the Canon is much less egregious because these latter at least CLAIM to be Catholic, and there's a non-condemned theological opinion that heretic Popes still must be deposed by the Church to fully lose office.  In fact, it surprises me that Bishop Sanborn would be an "una cuм" fanatic, since one could argue that if the V2 claimants materially hold the papal office, their names can be inserted there on those grounds.

Then, on top of that, even if the PRIEST decides to put the putative Conciliar pope into the Canon, this idea that for one of the faithful to assist at such a Mass makes then formal adherents to schism/heresy is absurd.  No Traditional Catholic is putting Martin Luther or "Patriarch" Kirill into the Canon, and there's no intent to adhere to any Conciliar errors, but it's related to their theological opinion about the Crisis.  Just as those Catholics, including St. Vincent Ferrer, who put the name of an Antipope from the Great Western Schism into the Canon, based on their theological opinion, did not thereby render their Masses sacriledgeous or sinful ... or assistance at it sinful, so too the same principles apply here.  If you were a Catholic who opined in favor of one of the other claimants at the time, you would not have been committing a sin assisting at St. Vincent's Mass, even if you knew he was wrong/mistaken, since the latter was doing what he did in good faith.

In fact, it surprises me that Bishop Sanborn would be an "una cuм" fanatic, since one could argue that if the V2 claimants materially hold the papal office, their names can be inserted there on those grounds.

Then, on top of that, even if the PRIEST decides to put the putative Conciliar pope into the Canon, this idea that for one of the faithful to assist at such a Mass makes then formal adherents to schism/heresy is absurd.

A lot of this is nuanced.  Catholics demand to know what's between your ears in order to have peace of conscience.

Could you or should you essentially preach as if the modernists lost their office, but Catholics are in a holding pattern until proper authority declares it.  You can objectively know a truth before declaration.

Quote

In fact, it surprises me that Bishop Sanborn would be an "una cuм" fanatic, since one could argue that if the V2 claimants materially hold the papal office, their names can be inserted there on those grounds.

Then, on top of that, even if the PRIEST decides to put the putative Conciliar pope into the Canon, this idea that for one of the faithful to assist at such a Mass makes then formal adherents to schism/heresy is absurd.

A lot of this is nuanced.  Catholics demand to know what's between your ears in order to have peace of conscience.

Could you or should you essentially preach as if the modernists lost their office, but Catholics are in a holding pattern until proper authority declares it.  You can objectively know a truth before declaration.

I put my words in quotes above.  Catholics have a variety of positions / opinions about the status of the Conciliar Popes ... whether a Cajetan opinion or a Sedeprivationist or full / Totalist SV position.  To claim that there's sin of blasphemy in merely inserting the name based upon one of these opinions is nonsense.  Traditional Catholics priests (outside the FFSP / Motu / ICKP variety) clearly demonstrate their lack of formal unity with the Modernist errors of the Conciliars simply by their very "apostolate".

Given the choice of attending a Mass with all outward appearances of being in Union with modernists and attending a Mass which is clearly an Alter against the compromise of Christ, which would you choose?

I understand that circuмstances vary, and that culpability varies.

Regardless of what they think, opine or vehemently insist upon, priests / bishops do not have any right whatsoever to omit the name of the pope in the canon of the Mass. No right whatsoever. The Church has always regarded ommiting the name of the pope from the canon of the mass as an act of schism, regardless of what anyone's opinion is in this matter. It is a very serious matter.

From Ex Quo (PDF attached):

"But however it may be with this disputed point of ecclesiastical learning, it suffices Us to be able to state that a commemoration of the supreme pontiff and prayers offered for him during the sacrifice of the Mass is considered, and really is, an affirmative indication which recognizes him as the head of the Church, the vicar of Christ, and the successor of blessed Peter, and is the profession of a mind and will which firmly espouses Catholic unity..."

The clearly teaches that the Mass celebrated una cuм not only espouses Catholic unity, it does so firmly, not only that, as is said below, the Mass una cuм is the chief and most glorious form of Catholic unity.
Which is to say that the Mass non-una cuм serves the purpose of being firmly divisive as is said below. It serves no other purpose.

Ex Quo continues....

"...This was rightly noticed by Christianus Lupus in his work on the Councils: “This commemoration is the chief and most glorious form of communion” (tome 4, p. 422, Brussels edition). This view is not merely approved by the authority of Ivo of Flaviniaca who writes: “Whosoever does not pronounce the name of the Apostolic one in the canon for whatever reason should realize that he is separated from the communion of the whole world” (Chronicle, p. 228); or by the authority of the famous Alcuin: “It is generally agreed that those who do not for any reason recall the memory of the Apostolic pontiff in the course of the sacred mysteries according to custom are, as the blessed Pelagius teaches, separated from the communion of the entire world” (de Divinis Officiis, bk. 1, chap. 12).

Pope Pelagius II who held the Apostolic See in the sixth century of the Church gives this weightier statement on Our present subject..."

Wherever you learned celebrating / assisting as the Mass una cuм was objectively a mortal sin, don't go back.

I could see doing this with a heavy dose of mental reservation. But wouldn't this be like putting in a lie right in the Canon of the mass.

It must be viewed as doing what we are bound to do, praying for him is following the law of the liturgy, the Law of Quo Primum - and for the sake of Catholic unity - and "if I don't say his name, I'm breaking the law and separating from the Church" - per Ex Quo.

Where did you ever get the idea that praying for him is a mortal sin or like putting a lie in the canon?

But he that shall scandalize one of these little ones that believe in me, it were better for him that a millstone should be hanged about his neck, and that he should be drowned in the depth of the sea. [7] Woe to the world because of scandals. For it must needs be that scandals come: but nevertheless woe to that man by whom the scandal cometh. [8] And if thy hand, or thy foot scandalize thee, cut it off, and cast it from thee. It is better for thee to go into life maimed or lame, than having two hands or two feet, to be cast into everlasting fire. [9] And if thy eye scandalize thee, pluck it out, and cast it from thee. It is better for thee having one eye to enter into life, than having two eyes to be cast into hell fire. [10] See that you despise not one of these little ones: for I say to you, that their angels in heaven always see the face of my Father who is in heaven.

Love of Christ is like love of your spouse.  The love which comes from the new religion is polygamy.

Consider the bolded, why must scandals come if not to test His elect and to separate the sheep from the goats, the wheat from the chaff, the evil from the good, ultimately heaven from hell.

 For this discussion, the NO religion is the scandal that God told us must come. It does good to always remember that God is the head of the Church, the pope is only the vicar, which is to say that everything is in the hands of God, not the pope, God sees it all and allows the scandals in order to test every individual. The pope needs the prayers worse than anyone, as such, it is injurious to him and us, and makes no Catholic sense to omit his name from the most efficacious and powerful prayer on earth.