Keeping the state out of religion means separating matters of state from matters of religion. Which means, in part, separating the business of the state from the business of saving souls. In modern secular parlance, this means motives don’t matter to the state. The state has business to conduct: creating conditions conducive to the pursuit of happiness. If the devil wants to help and has some good ideas - great! Don’t look a gift horse in the mouth.
As far as government policy goes, whatever works is fine with me. I don’t care if the boosters for a particular policy are in it only for the money, that they’re solely motivated by self-interest, greed, political advancement, salvation, selfless devotion to the common good, or pure compassion. Good people have bad ideas. Bad people have good ideas. The proof is in the pudding.