So in my game, the Yazidi faith declared itself no longer a heresy. It got control of Persia, which was then conquered by the Mongol Empire. The king of Persia remained Yazidi however, but because the top level liege was Tengri, the baba sheik declared a Great Holy War for Persia. They won, but Persia remained a vassal of the Mongol Empire and the title did not change hands. The old king remained in charge and pretty much nothing happened.