John Locke is oft-referred to, for good reason, as "America's philosopher." On how governments ought to treat their citizens, including and especially on religious matters, Locke matters.
And we can almost be certain that Locke was not an orthodox Trinitarian Christian. So that means he must have been something else. But Locke had a problem with putting his explicit religious cards on the table: In Great Britain in Locke's time, it was illegal to publicly deny the Trinity. Yet many did doubt or deny the Trinity back then. They just tended to, for safety, do it in private.
So Locke writes the book called "The Reasonableness of Christianity" where he sets out his ideal understanding of the common faith. Locke proposes a formula for defining who gets to be a "real Christian" as we might put that term today. And it's this: Jesus is a unique Messiah.
That's pretty much it (yeah, we can get into some other details, like you have to repent).
This simple formula got Locke accused by an orthodox theologian of being a Socinian. Because it's true that Socinians could pass Locke's test. But I don't think Locke was a Socinian. Rather he probably was some kind of Arian (this is what Locke scholar the late Paul Sigmund of Princeton told me, citing other Locke scholar John Marshall of Johns Hopkins).
So as it turns out Locke's orthodox critic probably was right that Locke was a unitarian, but wrong on which kind.
Still, Trinitarians, Arians, Socinians, Modalists, Mormons, Jehovah's Witnesses, and Swedenborgians among others all believe Jesus Messiah and therefore get to be "Christians" according to Locke's formula.
Or as John Adams described the American landscape, that implemented Locke's ideas, some time later:
... There were among them, Roman Catholicks English Episcopalians, Scotch and American Presbyterians, Methodists, Moravians, Anababtists, German Lutherans, German Calvinists Universalists, Arians, Priestleyans, Socinians, Independents, Congregationalists, Horse Protestants and House Protestants, Deists and Atheists; and “Protestans qui ne croyent rien.” Very few however of Several of these Species. Never the less all Educated in the general Principles of Christianity: and the general Principles of English and American Liberty."Socinians" actually made Adams' list twice. Most American Socinians probably wouldn't be imbibed in the "Racovian Confession," but rather influenced by Joseph Priestley's theology, which is a form of Socinianism. "Priestleyans" are Socinians.
I've heard people claim John Adams was an Arian, but I am not convinced. I know that Adams was a fervent unitarian, but of which kind I'm not sure Adams himself knew. He just "knew" the Trinity was false.