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Thank you for that. I too am considering this problem. Again, this may be self-deception, but I think I can come up with a counterexample.

I attend Mass in a disgusting hotel conference room. I know for a fact that protestant covens meet there for their false worship. Also all manner of secular events take place there. This does not stop our priests from offering Mass.

Long before the SSPX betrayal became apparent, anyone who went on Pilgrimage with them to Rome attended their Masses celebrated at Roman churches, by permission of the illegitimate authorities - churches long ago desecrated by the novus ordo false worship. I've never heard anyone ever complain about this.

When SV clergy travel to Europe, do they offer Mass in these once Catholic churches? Now I'm curious. I know for sure that they visit them.

Also, in hotel rooms, there take place the most obscene acts imaginable, and yet priests will stay in those rooms, and even offer Mass in them.

I've long held that it's not the problem of the faithful to determine or figure out whether or why the priest puts Bergoglio's name in the Canon, and that it's between God and the priest.  Faithful have a right to receive the Sacraments, and so they absolutely could go to Masses "una cuм" Cushing or now "una cuм" [whoever the next Antipope would be], or "una cuм" whomever St. Vincent Ferrer put in the Canon.  Padre Pio put Montini's name in the Canon of his Masses.

But this quote from Pope St. Athanasius II backs this up ...
While this refers in context to priests who were ordained by the heretic in question (after he became a heretic) ... the principle is that those receiving the Sacraments with the proper dispositions are not somehow infected or "injured" by the reception of them.

There were MANY Modernist/heretic priests around even before Vatican II, and those faithful who assisted at their Masses were not polluted, contaminated, or injured by their heresies.  In fact, if you refused to assist at such Masses due to your contention that Cusing's a heretic and his name was in the Mass, you would have been judged guilty of having committed mortal sin for failing to meet your Sunday obligation by any priest out there at the time for not assisting at the Mass.

And the question of "una cuм" isn't even one of heresy.  So, if you put the name in there because, say, you adhere to Cajetan's opinion that a Pope must be ministerially deposed by the Church before he loses office ... that makes you a heretic?  Last time I checked, Cajetan's opinion has not been condemned as heretical.  If you put the name in there because, while you have doubts, you feel you dont' have the authority to make that determination?  If you put the name in there because for one reason or another (which although mistaken is quite sincere and arrived at in good faith) you've concluded that the man is Pope, even if a very bad or even heretical one, who will be judged later by competent authority?  If you're a sedeprivationist and put the name in there because he's at least materially the Pope (dovetailing with the Cajetan opinion), are you a heretic and is that Mass sacrilegous and is it forbidden for the faithful to attend that Mass?  Answer to all of these is a clear no.

Interesting .... so .... does the Byzantine Rite consecrate on an altar stone?