Lockean theological rationalism itself deconstructs itself. Locke claimed "Revelation must be tried at the Court of reason," or something didn't he?? That raises the problem of historical authenticity, miracles and status of other faiths--not to say the problem of justifying the existence of a God a posteriori.
That pleasant Lockean empiricism gives way to Humean concerns, and Hume pretty much reduces ju-xtian scripture and theology to a strange historical footnote via a few paragraphs in the Enquiry. Believe if you will, but never mistake your religious belief for rationality itself (or as supported by evidence).
The followers of Leo Strauss have noted this and other contradictions in Locke's writings and conclude he was a Hobbes imbibed secret atheist trying to deconstruct revealed Trinitarian Christianity.
You can read Locke's Essay on Human Understanding, Chapter 14 where he discusses reason v. revelation here:
14. Revelation must be judged of by reason. He, therefore, that will not give himself up to all the extravagances of delusion and error must bring this guide of his light within to the trial. God when he makes the prophet does not unmake the man. He leaves all his faculties in the natural state, to enable him to judge of his inspirations, whether they be of divine original or no. When he illuminates the mind with supernatural light, he does not extinguish that which is natural. If he would have us assent to the truth of any proposition, he either evidences that truth by the usual methods of natural reason, or else makes it known to be a truth which he would have us assent to by his authority, and convinces us that it is from him, by some marks which reason cannot be mistaken in. Reason must be our last judge and guide in everything. I do not mean that we must consult reason, and examine whether a proposition revealed from God can be made out by natural principles, and if it cannot, that then we may reject it: but consult it we must, and by it examine whether it be a revelation from God or no: and if reason finds it to be revealed from God, reason then declares for it as much as for any other truth, and makes it one of her dictates. Every conceit that thoroughly warms our fancies must pass for an inspiration, if there be nothing but the strength of our persuasions, whereby to judge of our persuasions: if reason must not examine their truth by something extrinsical to the persuasions themselves, inspirations and delusions, truth and falsehood, will have the same measure, and will not be possible to be distinguished.
Locke also almost CERTAINLY was not a Trinitarian, but either a Socinian or Arian. When Locke posited his lowest common denominator -- the "essentials" of Christianity -- he simply said Jesus was the Messiah: No Trinity, no atonement, no orthodox doctrines. In other words his LCD included Arians, Socinians and Trinitarians -- they all believe Jesus was Messiah. He was accused of secretly peddling Socinianism. And his response was NOT "I am a Trinitarian," but rather a Bill Clinton-like "in my whole Essay, I think there is not to be found any thing like an objection against the Trinity...."
Remember during this time it was illegal to explicitly deny the Trinity in England and heretics potentially faced execution for doing so.
Let's leave aside the question of whether Locke were a secret atheist, which no doubt has huge implications for his teachings. What if Locke were simply a unitarian Christian who had a rationalistic method of supplementing the Bible with Truths whose essences are discovered in nature from reason?
Would that make him "not a Christian"? I think the answer is it depends on whose definition of Christianity use. While visiting a lecture at Princeton I discussed this issue with Princeton Professor Paul Sigmund and Jeff Morrison who was a fellow at Princeton's James Madison Program, but now teaches at Regent University. Prof. Sigmund, from what I understand, is a Christian and a political liberal. And he advocates religious based/Christian based arguments on behalf of liberal causes. He is a man of the "religious left" as it were. Jeff Morrison is a conservative evangelical. Morrison lectured on his new book about George Washington's political philosophy. And he noted that though Protestant Christianity clearly influenced Washington and that Washington was a lifelong Anglican/Episcopalian, the evidence that Washington was a "Christian" was ambiguous. Morrison noted this was because he believed one had to believe in the Trinity in order to be a "Christian" and the evidence for GW's Trinitarianism is ambiguous.
When I asked Prof. Sigmund's this question he noted his definition of "a Christian" was one who believed Jesus was a Savior or Messiah, something divinely special about him (even if it was just his mission not his person). That would mean Arians, Socinians AND Trinitarians [and in today's world Mormons and Jehovah's Witnesses] are all "Christians." And indeed all of the early Presidents from Washington to Monroe, including Jefferson probably were "Christians." Sigmund calls Locke, in no uncertain terms, a "Christian" yet he also believes (following Johns Hopkins Professor John Marshall) that Locke was an Arian.
The irony here is that America's Founding could be said to have a "Christian" political theology if one takes a more theological liberal, ecumenical, approach to "Christianity." "Civil Christianity" would incorporate not just Trinitarianism, but the unitarian heresies, folks who deny infallibility of the Bible, but who still believe certain "essential" parts to be divinely inspired, perhaps folks like the Mormons who add additional revelation. "Civil Christianity" might EVEN term religions like Judaism, Islam and ANYTHING ELSE "Christian" if the citizen behaves in a Jesus like way. Ghandi, for instance, may be a "Christian" accordingly.
However to the largely evangelical promoters of the "Christian Nation" thesis -- folks who view the Trinity as CENTRAL to "Christianity" -- the "Christian Nation" thesis fails. It is such a wonder that they are the ones who promote the idea of a "Christian Nation" so vociferously.