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Yes their are varied degrees of involvement of religion in different countries! Some are more some are less! Yes personal belief sets are also carried into government thats unavoidable

But what I’m referring to is more the authoritarian religious movements

I understand that but I'd still disagree, Religion is intrinsically woven into the fabric of all societies from top to bottom. It's more than personal belief , but even if it were 'just' personal belief, in a position of power this becomes the basis on which one would base decisions.