People talk about "church and state", but there are much more than churches involved. And, it is an issue that has been there since the first existence of organized religion within the borders of a secular state. But, it got more complicated.
Complications began when people tried to follow the same religion in different places which had their own histories, traditions and cultures. And that was only the beginning! How much authority did the state have over religion, and vice versa? At one time, people identified as clergy could only be tried in church courts, and held in church prisons.
Matters become even more complicated in modern times when religions and cultures mix together in many places worldwide.