My Mother inlaw is a Unitarian, and I think Universalist. I have attended church with her when she visits here. It is a very open, accepting group.
I found it very interesting. The Orlando group has a lesbian minister, and it wasn't exactly Bible based but it was comfortable and entertaining to say the least. If you attend you will not be hounded to convert and will be treated with respect and a nice welcome. They had a great music program with lots of talented people which is spiritual in its own right. They are also very community oriented, holding sales etc. to benefit those in need.
Good luck in your search.
r.