The Unitarian church of today has little to do with the Unitarian church of Jefferson's time. If you read Channings sermons, Adams writings, the Jefferson Bible, the works of Priestly,Theophilus Lindsey and other antitrinitarians you will see they were all on the same page. No Buddhists, no wiccans, no atheists wandering the aisles of the Unitarian churches back then. They all considered themselves Christians (many other Christians did not however).
The intent of Jefferson and others was to encourage religion, not limit it. The only restriction was that there would be no Federal church. All the founders agreed that a religious moral citizenry was essential if a democratically elected constitutional republic were to survive. The first amendment was an antitrust act of sorts, the purpose of which was to allow all religions to flourish and be vigorously debated in the public arena.
An analogous system was devised for the states. Federal power would be limited, experiments in democracy would take place in all the states and the best system would be, naturally, copied by others.
Btw... the lyrics of the Battle Hymn of the Republic were written by a Unitarian. I doubt a UU of today would pen the words the radical Unitarian feminist Julia Ward Howe did in 1861:
In the beauty of the lilies Christ was born across the sea,
With a glory in His bosom that transfigures you and me:
As He died to make men holy, let us die to make men free,
While God is marching on.