As a Christian who does NOT believe in the trinity, I think you are being ridiculous in thinking Unitarians are the ONLY Christians who do not believe in it. As a non-Unitarian Christian, I find the belief in a trinity to be absurd to my Biblical standards.
The doctrine of the Trinity is shared by Orthodox, Roman Catholic and every mainline Protestant church. 98% of all Christianity, by numbers.
The present-day Unitarian Universalist Church is well known for wearing its politics on its sleeve; it's left-wing, loud and proud. Combined with the political content of the scene, and recent Trek's unsubtle attempt to make thematic commentary on present-day American politics (see Paths of Disharmony), I find Mr. Mack's characterization attempt unsubtle, overreaching and out of place in Trek.
Trek's schtick was long just to ignore present-day religions for the most part; Gene Roddenberry was somewhere between agnostic and atheist and wasn't keen on churchgoing himself. I prefer that tradition, if any, about religion in Trek.