The French have a word, Laïcité, which doesn’t mean “lay” like you think it might by looking at it. Nor does does it mean “secular” like some dictionaries translate it as.
It means something very much like what you just wrote. Religion poisons politics, and politics poisons religion.
The French pride themselves on their spirit of Laïcité no matter how religious they are or how religious they aren’t.
I think we could learn from them.