Re: HRE electing a character or a country - it matters in instances where multiple countries are led by the same character, i.e. PUs, since those countries will still be operating independently in an IO rather than having a baked-in overlord-subject relationship.
I wonder if pops of different religions, classes and cultures will have different growth speeds (birth rates). Or maybe different "conversion resistance". I don't know if different religions historically had consistently different birth rates but there would need to be some way to ensure all jews aren't just converted out of existence within a century or two.
the western schism wouldnt be in eu4 due to time: irl it spanned from 1378 to 1418-19 when the council of basel (where Jan Hus also got burned as a heretic) took place. To explain briefly, it was a schism not really out of religious matters but political ones: france had forcibly relocated the papacy to avignon a while back, and what happened was that a newly elected pope tried to relocate once again to rome, only for a group of french cardinals to go back to avignon and elect their own pope there, which resulted in the catholic world being split between who followed the roman pope and who followed the avignonese pope.
