Religious influence will never completely die out, but in the sense you mean it, probably in the next 20-30 years.
I'm a spiritual person, but it disgusts me how religion tries to influence government policy in a regressive way.
So I am allowed to have ethics so long as I don't allow it to influence society? Good to know.
Well in an American context:
https://en.wikipedia.org/wiki/Establishment_ClauseThough admittedly "society" and "the state" are not the same thing, but it's undeniable that certain religious groups in the US do their best to get state-sanctioned power on their side (and are often, successful - particularly at the state and local levels).