Separation of religion and state is a big issue in Israel. But I can not see any source in Torah for this. Nor is it in the Constitution. "No national church" written in the Constitution of the USA is not the same as separation of church and state.
Still, in Israel I can see the point of this since the religious tend to be insane. [There is also the problem of group insanity besides individual insanity.] Even the thought that the religious authorities would have power gives me nightmares.
So why is this important principle not found in Torah? ANSWER: one of the reasons for the mitzvot is "shalom ha'Medina" (peace of the country), and experience has shown than power of religious authorities is highly detrimental to peace of the state and of the family, therefore one should have separation of religion and state.