I have another idea about to make religious Orders part of the game.
The Franciscans and Dominicans or Benedictians should be represented in the game. The ruler of a country (perhaps only kings or dukes) should be able to build them a church or a convent, in which there could be build a libraty or something similar to it. New Orders would need a permission by the Pope or become heretically. The Orders should give the country within a technology bonus and some more spiritual themes like the ideas in EU III. Perhaps a church holding could be given to a member of an Order, setting free new building possibilities in this holding and the opportunity to agree to a theological position. (Ok, the last thing might be too unserious for a PC game^^).
In analogy to this the Muslims should get the Law School's like Hanafits Hanbalits Schafiits and so on... working slightly different.
Also one should be able to decide, how to imprison a character: Either into the dungeon or the house arrest and the third thing. In my games, when I imprison a character he goes into the dungeon and suffers by bad health and the higher risk to die because of that. The player should have the opportunity to put the prisoner into house arrest.