I don't know how to quote multiple posts, but this is a reply to both you and Particle Mare.
There's a divide between how we, Unitarian Universalists, conceive of ourselves and how Christian denominations conceive of us. Unitarianism and Universalism are both older than the US Constitution, but union between those religions only came about in the 1960's. Unitarians rejected the concept of the Holy Trinity and consequently denied the divinity of Christ. Thomas Jefferson, for example, was a Unitarian, as was John Adams. Universalists, conversely, formed their faith mainly around the notion that all people would achieve salvation, regardless of the sins they've committed. Universalists could still believe in the Holy Trinity.
Since UUism is a composite of those belief systems, you can still be a UU and believe in the Trinity. Again, this is a concept I am coming to believe, not that I believe in necessarily. I've been exposed thoroughly to Catholicism in college and my exposure to both Catholicism and metaphysics has helped me gain an intellectual understanding of the Trinity, which I simply didn't understand at all in high school. At the moment, however, my conception of God is that God is the One and the souls of mortals are the Many; I believe that there is a distinct division between the One and the Many, though they are in close and inextricable relation to each other-- that's my central hangup on accepting that Christ was both Man and God.
As for believing in the Trinity and being Unitarian Universalist, there are many lapsed Catholics among us that still hold to Trinitarian beliefs. They're still accepted into Unitarian Universalism on the basis that that the search for personal truth is the highest tenant of our faith. Tangentially, this emphasis on personal truth is one of the key elements of the faith that ties us back to the Lutherans-- like the Lutherans, we believe that faith is a matter of interaction between the One and the Many and that it doesn't require the intermediary of a religious official.
Now as for Particle Mare's point, I'm well aware of the, well, persecution my faith has faced in certain regions of the country, for example, when pro-life activists disrupted one of our services and refused to leave, calling our church something like a "cathedral of Satan" or something like that. What I would argue is that people who would deny our religiosity do so out of a place of ignorance of the UU conception of Divinity and the way in which we interact with it.
Abject Divinity, as I understand it (and I believe Unitarians in general understand it) is as I implied a little earlier, the Eternal. Religion, to me, is the understanding of the relationship of the One to the Many, whether that's one person to all people, God to Creation, or the material subset of reality to the immaterial subset of reality. Abject Divinity is the unknowable constant to which we live our lives in parallel. Think of The Cloud of Unknowing. Central to UUism is the belief that everyone, divinely endowed with the Intellect and thus free will, has the capacity to choose between good and evil, belief and disbelief-- and furthermore that belief takes many names.
The Unitarian conception of Abject Divinity even allows atheists to practice UUism because for us Divinity is the unperishing and the unperishing includes the realm of moral ideals. Moral ideals can be held without the explicit acknowledgement of God supporting them. It is this logic that allows also to allow polytheists like Hindus into our fold-- one can conceive of Divinity as many gods, yet all those gods are united in their divinity and in a way a single entity.
Now, these abstracts apply to the practice of Unitarianism insofar as we as Unitarians believe in the inherent worth and dignity of all people and work to see that inherent worth and dignity realized. Thus, we marry LGBT couples in a religious context on the basis that LGBT people should be allowed holy union. We fight poverty and systemic racism on the basis that the poor and minorities are just as human as the wealthy and the majority and deserve the same rights from both a secular and a religious perspective.
Because secularism is something many Unitarians tend towards and because the religious philosophy of our faith tends more towards the abstract and the philosophical, it's easy to mistake us for an irreligious group, but that patently isn't true. There are beliefs that even atheist Unitarians need to hold in order to be called Unitarian-- you won't find any Randian objectivists among our faithful, for example (at least I haven't met any).
Sorry for the wall, but I felt like these questions needed much longer answers.