Well, they certainly considered themselves Christians, and protested quite vociferously when accused of not being Christians, usually by competing "orthodox" clergy.
It all came to a head around 1815, when William Ellery Channing---generally regarded then (as now) as exemplary of that era's unitarianism [Abigail Adams specifically endorsed Channing theologically]---answered some prevailing charges against unitarianism in
A Letter to the Rev. Samuel C. Thacher on the Aspersions Contained in a Late Number of the Panoplist, on the Ministers of Boston and the Vicinity.
Now, perhaps the defining feature of unitarianism was that it didn't believe in the Trinity---1 + 1 + 1 would equal Three, not One. Hence the term "unitarian."
There were other orthodox doctrines rejected, too, namely, as Channing wrote:
"I fear, that the Author of the Lord's prayer will, according to this rule, be driven as a heretick from the very church which he has purchased with his own blood. In that well known prayer I can discover no reference to the "inspiration of the holy scriptures, to the supreme divinity of the Son and Holy Ghost, to the atonement and intercession of Jesus Christ, to the native and total depravity of the unregenerate, and to the reality and necessity of special divine grace to renew and sanctify the souls of men;" and these, let it be remembered, are _five_ out of the _six_ articles which are given by the Reviewer as fundamental articles of a christian's faith."
So that's what they didn't believe. So what did they believe? Channing wrote:
"The word UNITARIANISM, as denoting this opposition to Trinitarianism, undoubtedly expresses the character of a considerable part of the ministers of this town and its vicinity, and the commonwealth...We both agreed in our late conference, that a majority of our brethren believe, that Jesus Christ is more than man, that he existed before the world, that he literally came from heaven to save our race, that he sustains other offices than those of a teacher and witness to the truth, and that he still acts for our benefit, and is our intercessor with the Father. This we agreed to be the prevalent sentiment of our brethren."
Is that Christian enough? Certainly not to the orthodox clergy and various laymen of the time who stood in opposition to them.
Probably not Christian enough for most Christian theologians of any stripe today, certainly not evangelical or orthodox.
But perhaps Christian enough for the sociologist or the historian. "Unitarian Christian" is my own preference, both descriptively and definitively, at least for our best understanding in this day and age. [Channing and others used "'rational' Christians," but in our day, I'm not sure that's helpful or descriptive enough, although it's certainly a proper term. Channing himself published a popular tract in 1819 called Unitarian Christianity.]
Do read Channing's letter for yourself, as there's more than can be sketched or excerpted here. It offers an excellent window into what is called the Unitarian Controversy today, and clearly outlines the issues and the players, a clarity we need to consider the unitarians properly in the scheme of things.