I also attend a Unitarian Universalist church. They admit that they have their original roots in the Judeo-Christian tradition. However, they do not seem to share the dogmas which most other churches with those roots. The Bible is viewed generally as a collection of documents written by many authors, containing much that can be labeled 'wisdom' and much other material of historical interest as a reflection of the views of the authors, but not necessarily absolutely true. So, the minister may quote Jesus at times, in encouraging the congregation to demonstrate love for one another. The minister would be extremely unlikely to quote Paul where he states that women should remain silent, that the man is the head of the woman, etc, as this is not seen as an inspired expression from God, but simply Paul expressing his opinion, as Paul himself admits (speaking on another topic) at 1 Cor 7:25.
Sermons at the UU church I attend are just as likely to quote from other sacred books as from the Bible, so the congregation is exposed to the wisdom contained in the writings of Buddhism, Islam, Taoism, as well as individuals such as Einstein, Ghandi, Starhawk, Black Elk (all of whom are contained in the UU hymnal), as well as many others. There have been services honoring the various traditions mentioned, as well as a few with a distinct neo-pagan flavor.
While a JW, one is exposed to a single narrow view, claimed to be that of the only people on Earth to whom God ever revealed himself. In contrast, at the UU church, the view is more like: God, however one chooses to define the term, would logically be equally accessible to all people, in all nations. Each nation, even each individual may have a unique perception of 'God', which may be equally valid. Some view 'God' as very close to the classical Judeo-Christian image, others have a more abstract definition, some don't believe in 'God' at all. UU's feel that just because someone has a different perspective, this does not have to be grounds for division. There is a word in one of the traditions, 'Namaste', which means 'I honor the sacred within you'. This word is sometimes used as a greeting, in which we recognize that other individuals often have differing views, we try to look for the things we share in common, and build on those things, rather than focusing on our differences.
Bright Blessings
gaiagirl