There's no doubt that religion and politics mix. They're built on each other.  Judeo Christian scripture is the story of people living together, being powerful and fair together, governing themselves, etc as if there were a God entity of some sort. The history of the Christian religion is simply a version of the history of western civilization. Likewise, western democracies, though they may have grown and progressed along the lines of reason, are actually built on the work and the hopes and the courage of people of faith.

So, with so much rootedness in common, it is hard to say they are a bad mix. HOWEVER, governance must pass the tests of reason, along with the convictions of people that they have come to by experience. 

Western societies are losing the ability to hold religions to account. Religions get treated as antiquated houses of superstition, or people simply ignore them, which allows wing nuts to pose as religions. Religions, themselves, must stop whining about their rights.