I've seen a faction with 2 crosses that was "taken back into the fold" by the Pope. Quite funny, because in the before turn I had taken two cities and wiped out like 1/2 of the troops. It is likely related to how much beating it takes, because I have seen factions with 5-6 crosses that did not get reconciled until a few turns later when the pope died; and they were very aggressive (Milan slaughtering the French)

Does your Papal approval rating influence how much hit the other nations take if they commence hostile attacks upon you? Or is it just for calling crusades and getting them approved more easily?