I believe so, the rules say IF a lot
● Map Card Change. A victorious crusade flips the Map Card if the other side is Catholic. A victorious jihad flips the Map Card if the other side is Islamic. A victorious reformation flips the Map Card if the other side is Reformist. Transfer all Ruling Class to the same Cities on the other side
Although please note:
● The Bloody Rule. The Religious War cannot be triggered if there are no Heretics to kill in the target Location (neither Heretic Ruling Class nor bordering Heretic Pirates).
What Mike Ricotta said.