I think political Conservatism is based in rigid rules for behavior, rules-based and formula-based thinking, often accompanied by fear and hate based attitudes, and is popular with religious people who need to feel they are right or superior to other people who do not share their beliefs. Progressive politics tends to be more common in people who have inclusive and tolerant attitudes regarding others' beliefs, lifestyle preferences / social and religious practices; and who maybe are more content not to have explanations and answers to every question, and who would prefer to trust others more than fear them.

I would expect more openess to the non religious as you move to the left. can't generalize though. I have been an atheist since forever myself. It was too hard to believe.

Well there definitely a link which anyone who is even glanced at the stats can see. Conservatives tend to be religious while liberals tend not to be. Like most things involving people it is not absolute.

If you read oxford's history of the American people the author talks about his theory that progressive politics and pulpit politics have been in conflict since the beginning of this country.

I have gotten more leftwing as I went away from faith but a human lifespan is ling so maybe I will reverse again haha.

I've always been a liberal and a non-believer since my teens. No changes here.

I'd assume they are positively correlated but correlation doesn't imply causation.

Atheists have typically thought critically about belief, god, religions etc. Progressives have typically thought about how government policies impact other people. We are willing to take a minority view because we have weighed the evidence and believe our views to be in the best interest of all.

Many religious people, not close to all, have religion so ingrained that they may not apply critical thinking to it as it doesn't occur to them, they accept it on faith. Perhaps because they accept religion on faith, they are more likely to accept other things on faith.

Obviously there are lots of exceptions to these overgeneralizations. Smart thoughtful people are on both sides. Food for thought.