Have not played that many times as a non-catholic faction but each time I played as the Turks a crusade against me was called each time I seized Constantinople ...

My one time as the Egyptians, crusades were called for almost from the very start of the game (but no catholic faction obliged) and a second time when I had invaded Sicily and Naples (wonder why the fuss ... ) Needless to say that a two turns later St-Pieter had become a very Mosquee

When playing as a catholic, call for crusades agaisnt the Eggy and Elmo are common occurrences but I usually am too busy with my own agenda to bother ... If I get excommed, a crusade against me is usually called the very next turn and suprisingly enough my excommed king seems to live until he is 68 to give everyone time to organise ... On the other hand, if a start a crusade againt an excommed catholic faction, their king dies at soon as he hits 51 or manages to get killed in battle the next turn (makes me wonder if my PC has a soul .... the soul of a cheating b...d anyway )

One this I for sure do not recommand is a crusade against rebels ... The IA catholic factions are smart enough to conquer the province for one turn just for the fun of seeing my crusade fail miserably. An obviously smart move so no reason to complain but painful the few times I tried ....