I'm getting back to my post after testing some things during an Antioch campaign. Maybe this can help.

Winning a Crusade boost your Papal relation to the maximum (10 points).

It seems that having a settlement with Catholic below 50% decrease your Papal favour by one every 2 to 3 turns.

To maintain your relationship with the Pope you apparently need one building from the religion tree in every city.

yeah well i got majority christianity in all cities ive done a succesful crusade and im constantly killing muslim armies and sieging and sacking their cities as Koj and i went from standing 10 to 1 before there 6th crusade was even announced. i dont get it, ive not broken any treaties or attacked any other catholics. i have no idea why the pope despises me. also all his religios requests have so far been literally impossible to complete because i cant hire assasins and killing the targeted army doesnt count for somereason and the other requests have been building some catholic buildings within 3-10 turns that would require 100+ turns to unlock. seems like total ♥♥♥♥♥♥♥♥ to punish me for being extremely succesful in everything else so artificial difficulty must be introduced to stop me somehow and make me a target for cancelling my trade routes and alliances with other catholics? honestly it just feels like a bug but im guessing its not because theres so many other people complaining about this around the forums.

my standing also with the papal states is 360 cos i gave them about 100k in gifts but every single turn its goes down ive assasiated 3 kings in 10 turns cos of excommunication and in the papal standing it keeps saying that my relation to the papal states is so fking low i must be excommunictaed xd almost 400 and its not enough this cant be right....

i have the same problem, i cant complete assasin missions they just get aborted