Medieval priests whose primary concern was the priesthood still took up arms. It was not their primary function, but they did not stop being a priest; Adhemar le Puy did not stop being a Bishop and become Sir Adhemar while on Crusade.
He did remain ordained, and as I say that's not a problem as he can be of any religious rank (even Elder Rank).
However, he was not preaching in his parish church
while he was swinging a sword. If you have a sword in your hand, you're a warrior.
In real life he could switch from one to another in 5 minutes if needed. In BM, you cannot switch more than once every 7 days. That seems reasonable to me given the turn structure of the game.
