Well, Putin has created the symphony of church and state in Russia. It really doesn't have to be one or the other, that's Communism.
There was no Russian John Locke or Frederic Bastiat.
And most Russians were serfs up until 1861.
Haven't said that, even Russia has formal separation between church and state.
Non-Orthodox Russians have the same legal rights as everyone else in that country.
As for the broader question of the relationship between church and state, the U.S founding fathers had the right idea IMO:
Freedom of, and Freedom from Religion.