You mean two great saints who stuck with the Holy See through thick and thin? What do these great saints have to do with self-serving schismatics like Pivarunas?
A pope can become a schismatic if he falls into manifest heretic?
You confuse schism and heresy - one has to do with the Church's organizational authority and the other has to do with the Church's teaching authority.
No Pope has ever taught heresy ex cathedra and no Pope can do so, by definition.
What about the so-called Papal Schism of the 14th century?
It was not a schism, as you yourself acknowledge by labelling it "so-called."
Who was the schismatic then because there were rival claimants to the papacy?
In each case there was a legitimate claimant and an illegitimate claimant or sometimes two.
The illegitimate claimants were, of course, in schism.
Sometimes, resistance to heresy is preferable to submission to heterodox bishops and clergy.
One can resist heresy without committing the mortal sin of schism. You yourself provided signal examples: Athanasius and Maximus.
Besides, your argument is one of an ad hominem attack that doesn't rebut the substance of Bishop Pivaruas's arguments.
You are confused as to the meaning of the term ad hominem - if I call a Communist a Communist in a economic discussion, it can be considered ad hominem because being a Communist is a pretty bad thing to be. However, "Communist" is also descriptive - it indicates precisely the set of flawed economic assumptions the Communist holds.
Likewise calling a schismatic a schismatic in a theological discussion is not just an epithet but a descriptor.
Sometimes schism is a necessary evil if it preserves the faith of the faithful.
If you think that it is ever "necessary" to do evil - that is, to commit the mortal sin of schism - then you have much to learn about orthodox moral theology.
That necessity, thus mitigates the mortal sin of schism.
There is no demonstrated necessity whatever. This is special pleading.
He is a valid, but illicit bishop.
What proof have we that he is a valid bishop? The word of another schismatic or two?
I certainly don't take his word for it.
Where the bishop is there is the Catholic Church. (St. Ignatius of Antioch Letter to the Symrneans.)
Ignatius was clearly referring to a validly and licitly consecrated bishop accepted by his brother bishops - not renegade schismatics.
Try reading the Fathers in context, instead of prooftexting them Protestant-style.
St. Maximos and St. Athanasius were NOT in communion with their bishops. St. Athansius was NOT in communion with Pope Liberius who arguably was an Arian.
Address the content of his arguments. Pivarunas is a Thuc bishop.