Had you and I been forty days with Moses on Mount Sinai and admitted to behold, the divine Shekinah, and there told that one was three and three, one: we might not have had courage to deny it, but we could not have believed it. The thunders and lightenings and earthqu[ak]es and the transcendant splendors and glories, might have overwhelmed us with terror and amazement: but we could not have believed the doctrine.
But why the "unitarian controversy" matters much to some people, I don't know. Samuel Adams, John's cousin and his virtual co-leader in the early days of the American Revolution, was a Trinitarian, and John and Sam's political theology differed not at all---whether you believed Jesus is God or not didn't make any difference.
The other thing about John Adams' unitarianism is that it was expressed in private letters like these, after he left public life. As a public man, as president, what did America know of John Adams' "unitarianism"?
The answer is, little or nothing.
President John Adams' 1798 thanksgiving proclamation explicitly recognizes God the Father, Jesus the Redeemer and the Holy Spirit:
"I have therefore thought fit to recommend, and I do hereby recommend, that Wednesday, the 9th day of May next, be observed throughout the United States as a day of solemn humiliation, fasting, and prayer; that the citizens of these States, abstaining on that day from their customary worldly occupations, offer their devout addresses to the Father of Mercies agreeably to those forms or methods which they have severally adopted as the most suitable and becoming; that all religious congregations do, with the deepest humility, acknowledge before God the manifold sins and transgressions with which we are justly chargeable as individuals and as a nation, beseeching Him at the same time, of His infinite grace, through the Redeemer of the World, freely to remit all our offenses, and to incline us by His Holy Spirit to that sincere repentance and reformation which may afford us reason to hope for his inestimable favor and heavenly benediction..."
Bold face mine. As we see, the Father is in there, Jesus is still the "Redeemer," and the existence of the Holy Spirit is acknowledged, not denied. The Trinitarian formulation.
Most people, whether in 1798 or in 2019, would read President Adams' proclamation as explicitly "Christian," explicitly in harmony with Christian orthodoxy. What John Adams believed in private is of some interest, but it is of little importance. These days, we use the term "Judeo-Christian" specifically to dispose of the question of whether Jesus is God or not anyway. And as we see here, in public, President John Adams comes off as more Christian than that minimum, not less.