Use of "separation of church and state" in non-Christian countries

You can replace church with religion, and say “separation of religion and state”.

The word church in “separation of church and state” is not referring to the building used for Christian worship, or to a Christian organization, though. It is used to mean “an institutionalized religion as a political or social force”. In this sense, it is more specific than religion, but it is also more generic than church used in reference to Christianity.

“In political terms, secularism is a movement towards the separation of religion and government (often termed the separation of church and state).” —Wikipedia

An online search shows that separation of mosque and state is indeed being used. Really what these phrases are talking about is having a secular government. A generic phrase would be separation of religion and state.