Personally, I think an "Atheist State" should still allow freedom of religion but promote Atheism throughout the schools etc. to stamp out religion, at least among the new generations, and make it an embarrassment to admit you're religious in any way. Churches and religions will not be allowed to create private schools and will stop being supported by the state in any way, whether this means cutting off funding to churches or removing all mentioning of "god" from the national anthem (which, ironically, my country has even though we are largely non-religious). Hardline clerics and elites should be suppressed, the Pope removed from his position etc.