Most importantly, you are an easier target for other rulers (assume lower cost in prestige to grab/usurp titles, lowered badboy?)
For sure, many other characters will dislike you, especially the zealous, the ecclestially educated, the crusaders, and many othes. The loosers will like you! FOr example the scepticals, the heathens, the bastards, the kinslayers. So if you´re trying to create an empire with these guys as vassal, try to get excommunicated. Should make for an interesting game.