Christianity does not exist in BattleMaster. There is no one dominating worldwide religion.
Thus, any argument of the form, "We should do _____ because that's the way Christianity behaved" is, at best, highly suspect.
There are already penalties for not sharing the religion of your peasants, and adding more penalties will not make people care more about religion. Nothing the game mechanics can do will make people care more about religion.
I wouldn't say nothing, but I would say no penalties.