The Antipopes Stick

What if the Catholic Schism stays, and there is three divisions of the Catholic Church, in Avignon, Rome, and Pisa?
 
Eventually that would probably lead to three different "Catholic" churches, all not recognizing the others and believing themselves to be the true Catholicism: Avignonese Catholic Church, Roman Catholic Church, and the Pisan Catholic Church. This could prove to be just as divisive as the Protestant schism.
 
Seeing as the antipapal schism was resolved more than a century before Protestantism developed, I think it's fair to assume that ITTL Protestantism as we know it will be butterflied away. But I could see a movement of Christians who are disgusted with the corruption and whatnot of three separate popes, and advocate the return to a single pope ruling all the Catholics. However, as they will differ on their opinion as to who is the rightful pope, it could get just as ugly.
 
How might Protestantism fare?

Perhaps the rival popes shelter each other's dissidents?

Depending on how much influence these dissidents have in their new homes, there might eventually be doctrinal divergences among the three churches.

Plus Protestantism, split up as it was, often became rather statist--Luther did PR for the German princes, Calvin ran his own little Iran in Geneva, and the Anglican Church supported the English monarchy (one cleric said that Elizabeth, by forcibly imposing religious uniformity, was only doing as Moses did).

A split-up Catholic Church, particularly one in a strong state like France, might be more vulnerable to the exertions of kings and we might have Avignonese-Catholicism becoming a French state church much like Anglicanism was in England. And in a weaker state, you might have the church dominating the government.
 
Or there could be a mixture of protestantism and Catholicism in Europe, the Protestants develop due to the wars between Avignon and Roman Catholics
 
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