depends on if you mean the people or the faith, I guess.
The other poster is correct, you will just have to visit a few to see what you like.
Ask some democrats in your area where they go to church.
For instance, I'm in DFW..and I have a friend who is a minister and an outspoken Liberal Democrat like some of the Christian Right are...and his wife is a Democrat and a local Judge. They are Methodists, it think.
I grew up in Unity, not Unitarianism, but Unity.
http://www.unityonline.org/ You can find a local church most places.
I still go sometimes.
I'm in Christian Science now. Depends on who to talk to there, but I've had nothing but loving experiences.
I'm into Christian Metaphysics, so I tend to gravitate to those type churches.
Also, you might check to see if there is a "gay" church group or congregations that really do welcome ALL. There are several in Dallas/Fort Worth. I like those congregations because they really do a lot of good for people in general. The man who married me and my husband is gay (we don't have ministers in Christian Science), and I picked him because is is such a great guy, and right on track every time I hear him speak. He has such a sweet, loving spirit. He used to have his own church, but now he's in Unity.
so just look around...I bet you can find something.