One thing to note though: One Unitarian-Universalist church can be really different from another. In the city where I live we have both a Christian-ish UU congregation (although they won't make you swear by Jesus to get in or any of that) and a secular humanist athetist UU society (they won't even use the words 'church' or 'sermon' to describe themselves). So it might take a few tries to find a UU where you fit in.

I'm currently at one that's kind of in the middle. We use Beatles songs and religious-themed filks as hymns, but the sermons still include a good amount of biblical symbolism.