Aha - two birds, one stone. I had considered the English Civil War, but that conflict has more to do with the extent to which the King was able to exercise personal authority in the governance of the state. Parliament was not happy about that, and so....
No, I was thinking of a theologically-motivated conflict in the sense of "you are no longer fit to rule because your interpretation of this holy book - which forms the basis of our legal and governmental systems - is not in accordance with ours. When it comes to the state religion, you're doing it wrong, and therefore you must go."
My suspicion - although, again, I confess my ignorance - is that the clearest examples of this are to be found somewhere in Islamic parts of the world, either with the usurption or founding of caliphates, or in more sectarian divides such as that between Shia and Sunni interpretations of Islam.
Does that clarify things?
BM
I am aware of no circumstances in which a theological disagreement led to a revolution or rebellion against a sitting government. But then, I find it impossible to define an argument as theological - academic versus economic, power-based, etc - when it comes to government. Sorry.