Britain fought several wars over this question, and the answer there seemed to be "yes." But I'm less familiar with the the history of continental Europe.
Was it solely a Catholic/Protestant feud that required monarchs to be part of the state church, or would an Eastern Orthodox monarch also be required to convert prior to assuming office?
Would it have mattered if the King of the Netherlands, for example, were a member of Lutheran denomination rather than the Dutch Reformed Church (i.e. would it have been enough for him to simply not be Catholic?)
Were there examples where membership of the state church was not technically required, it just never happened that the monarch was of a different religion?
Are there any examples you know of in which a European monarch was of one religion or denomination, and his/her subjects (or the state church) subscribed to another religion or denomination [and the situation didn't end in an overthrow of the monarch in question]?
Thanks in advance!
"Are there any examples you know of in which a European monarch was of one religion or denomination, and his/her subjects (or the state church) subscribed to another religion or denomination [and the situation didn't end in an overthrow of the monarch in question]?"
The best example of this is King Henri IV of France. Originally raised a Protestant by his mother (he wasn't meant to end up with the throne), and who repeatedly fought for the rights of Protestants within France (which did not go well), when the opportunity to become King of France finally arrived, it effectively had the condition that he convert to Catholicism. The Catholic population was still the majority at the time, and the people were not willing to have an openly Huguenot king.
So he converted, with the famous quote "Paris is worth a Mass". What he personal beliefs were afterwards isn't really known, at the very least he seems to have paid consistent and convincing lip-service for the rest of his life.