Quote Originally Posted by Quillan
Voice of experience from playing Byzantium speaking: attacking units of a catholic faction, regardless of circumstances, causes a lowering of the relationship status with the Papal States faction. Too low a relationship with the Papal States results in crusades called against you. Therefore, it is beneficial to war only against excommunicated catholic factions when you are still on good terms with the papacy. They do not always give you a choice in the matter however.
Some counter-experience here. In my Byzantium campaign I fought constantly with Venice and Hungary, but had a decent relationship with the Papal States right up until I sneak attacked them. Taking Venice, even with a Venetian pope, did not significantly affect my standing with the Papal States.

Touch one of their precious crusades, though, and your relationships with all catholic factions plummet.