If we are, as our sign states, "A Community Church in the Christian Tradition," and if we do not place a doctrinal requirement upon our members--that is, if we do not define what a Christian believes--then how do we describe our place in the UCC? As I have mentioned before, in the context of Eliot Church it is perfectly acceptable to be an atheist and consider yourself a Christian. In fact, it is not uncommon. Does the name "United Church of Christ" imply in our context that some of us are "more Christian" than others?
Furthermore, the older term "Congregationalist" is sometimes thrown around to describe our UCC affiliation. However, the UUA is also part of the Congregationalist tradition and when we use the word to describe a specific denominational or associational structure, it is most often used to indicate a third group: the National Association of Congregational Christian Churches (NACCC). They are fine folks, but we are not at this time affiliated with them. The word can be found in the names of congregations affiliated with the UUA, UCC, NACCC (linked above), as well as the Conservative Congregational Christian Conference (CCCCUSA). That's quite a range in theology!
Anyway, it just shows how tricky words can be. It is hard to be precise, sometimes. At our church we assume that you can be a Christian and not a Trinitarian. Also, the Unitarian Universalist Association of Congregations is as much "Congregationalist" as the UCC. Therefore, in a moment of linguistic weakness I am left with "our trinitarian connection."
How strange... I will look for something better.