Once again, "secularism" is not a synonym for "atheism", "irreligion", or any other term that has to do with a lack of religious belief. It is notable that the initial headline that appears on the main page of Huffington Post's religious section, "Is This The Secular But Spiritual Person's Church?," changes to "Unitarian Universalists See Chance For Growth In Growth Of Secularism" when you actually go to the piece. Notice the discrepancy and its implications.
It is yet another example of the pervasive bias and distortion of what secularism actually is. Secularism in no way infringes on the right of an individual to believe what they want. Though it is true that among secularists, non religious (not necessarily atheists) make up the majority it does not mean that religious people cannot be secularists. Many are. The person who leads Americans United for Separation of Church and State, one of the most prominent secularist groups, is the Reverend Barry Lynn. That one particular denomination finds secularism useful to them is not really that significant in and of itself. It is interesting and in some ways hopeful but still cannot change the basic meaning of Secularism.
For the record, Unitarian Universalists are no more unified than any other denomination. Overall, they are fairly liberal in their outlook but they do vary within that framework. I have met UU members who are agnostics and atheists and others who believe in God as wholeheartedly as any other Christian.