This post does not concern the UU denomination, but focuses rather on classical unitarianism, the kind that came forth in New England in the 19th Century. These Unitarians diverged from conventional Christianity primarily if not exclusively in their rejection of the Trinity and/or the divinity of Christ.
This tradition has a long and honorable ancestry. Special mention here will go to:
The development of the Trinity at the Council of Nicea (325) was in large measure due to the rivaly between Christians who considered Christ, the son of God, as equal to God the Father (called Athanasians) and the followers of Arius, who believed that Christ was created by God.
Although the Council is generally thought to have settled the matter, that is not entirely true. The Arian party went into eclipse-- temporarily. Constantine, who had supposedly chosen the Trinity, soon changed his mind-- several times in fact. On his deathbed he was baptized by an Arian priest.
Over a period of time the Athanasians maintained the place of power in Rome and made the Trinity an obligatory doctrine for all Christians; they considered the Arian Christians to be 'heretics'. Meanwhile most of Europe was being evangelized-- by Arians.
In 410 the Visigoth, Alaric, an Arian Christian sacked Rome. His damage to the city was minimal, and he allowed the Roman religious authorities to continue with the activities of their church.
The Arian Visigoths and Vandals settled in North Africa where warfare between Arian and Roman Christians ensued for many years. The Romans eventually attained dominance, but "heretical" Arian Christians sprang up in various places in Europe throughout the history of Christianity. Look for example at Socianism.
Mohammed is not commonly thought of as a unitarian, but his rejection of what he perceived as polytheism had a prominent role in the origin of his rival faith.
'Political theology' had played a big part in establishing the Nicene Creed and the Trinity. The same kind of political theology played a similar role in Mohammed's rejection of it: since Alexander the Great various human gods had been imposed on the Arabian and other Eastern cultures who came under Alexander's Empire. The deification of Jesus must have appeared to the Arabs much like the deification of Alexander and other 'god pretenders'; Mohammed chose strict monotheism: There is one God; his name is Allah. (Allah is the Arabian word for God; it is used by Christian Arabs as well as Moslem ones.)
Mohammed, and his followers, venerated (and still venerate) Jesus; they consider him the greatest of prophets after Mohammed. They consider Mohammed the last prophet: God had ordained that henceforth he would be worshipped in the ways Mohammed had designed-- and no other (not really that different from most Christian authorities!). Part of Mohammed's design was that Jesus will appear again at the last day.
A relatively small splinter group of Moslems believe they have directions from God to conquer the world and make it-- Moslem. A similar number of Christians have very similar ideas about their God.
The two best known early unitarians in England were Isaac Newton and John Locke.
In the 19th Century Unitarianism became one of many Christian denominations; The primary problem they had with conventional Christianity was trinitarianism and the deity of Christ.
John E. Clayton, my grandfather, was a founding member of the Unitarian Church in New Orleans, Descended from a long line of Quakers, then Methodists he left rural Concordia Parish as a young man to study law.
In N.O. he followed in the footsteps of Emerson to reject the Trinity-- and the divinity of Christ.
While he was there my father was born (1897). After getting his law degree he returned to practice law and politics in Concordia Parish. Becoming tubercular he took his family to Roswell and died there.
Many years later I passed through Roswell. I found his grave in a large Masonic lot, empty except for his body. I had an impulse to direct my own remains to that spot-- to keep him company. I am a unitarian in the sense that he was.