How do I find an accepting healthcare provider?

I just moved to a new area, which is right on the border between a red state and a blue state (living on the blue side, of course), and I'm looking to set up healthcare appointments. I can search for providers through my insurance, but there's basically no information on them. I would expect that the average medical professional would be more accepting than the average person, but I would still like to increase my chances of finding an accepting provider, since there are definitely phobes around. Are there any tips I can use to help with that?