moish01, it depends on how they enforce that rule. If they have spare hats outside the bais medrash so that all visitors without hats can borrow one for davening, fine. If you refuse to take the hat, then they refuse you entry into the shul. If they don’t have the means to help people off the street comply, then I agree it’s a bit wacky.
I was once in a shul where the minhag hamakom was for all men and boys to wear a tallis. I accepted the tallis they offered me. My friend did not, and was asked to daven in a different shul where the minhagim are to his liking.