So far as I can tell, “religion in politics” means that people vote and so on based on what they think the world is actually like, how we know things, what the point of life is, what makes life good or bad and so on. What’s the purified alternative to that?
Use Reason, of course.
The alternative is to vote based on academic sociology/economics/etc. and deductive reason.
If the only valid knowledge is through science and particularly science done by left-wing intellectuals), then basing your choices, especially choices that compulsorily affect others, on anything else is at best irresponsible. This is a natural effect of the politicalization of culture. Just as the logic of government is to expand, the logic of politicalization is to eventually make epistemology a political matter. The ultimate goal is to make certain political conclusion un-concludable.