Great data and thanks for that website. Suprising amount of Unitarians but it has always been popular amoung the Elites thanks to John Adams.
It's also worth noting that it seems like Unitarians were mostly appointed during the years where it was a bit more of a fad:
1812
1858
1862
1882
1903
1921
1943
1945
While there were obviously Unitarians before this (within Protestant denominations), the American Unitarian Association (which largely spun out of Congregationalism) began in 1825 and lasted until 1961. By the time it merged with the Universalist Church of America in 1961, it was more or less a pointless collection of extremely liberal churches that didn't have any real theological convictions ... hence it merging with a group that inherently actually has NOTHING to do with being Unitarian, haha; you can be a Trinitarian Universalist, of course.
I think Unitarianism was only especially popular in a society where you felt cultural pressure to be a part of an organized Christian denomination but you were extremely theologically liberal. In an America after the World Wars, I think its days were extremely numbered, and you then of course see no more Unitarians on the Supreme Court in the second half of the Twentieth Century.