Whether Locke was a "Christians" depends on how that term defines. If it means Jesus was 2nd Person in the Trinity and the Bible is inerrant or infallible, Locke was not provably Christian (and I doubt he was under this definition).
If it means Jesus was Messiah (regardless of whether he was 2nd Person in the Trinity) and the Bible is, in some sense, God speaking to man, then yes, John Locke was a "Christian."
Locke is important because if modern liberal democracy is to have any kind of Christian political theology, it is of the Lockean understanding. I have some controversial and modest ideas on modern liberal democratic political theology. The more controversial thesis is American political theology is "not Christian." The more modest is the notion that the "rational Christian" political theology of the American Founding is not only non-Trinitarian, but non-creedal. The Bible may be, in some sense, God speaking to man, and Jesus the Messiah, but the stuff of creeds (that Jesus is 2nd Person in the Trinity, the eternally begotten Son of the Father, while being God Himself, that "these" are the exact books of the biblical canon) is fluff.
You may think Jesus is the 2nd Person in the Trinity because the Bible says so. And you are entitled to your "opinion." But "rational Christian" political theology consigns that notion to the realm of "opinion" not "knowledge." And "rational Christian" political theology traces to Locke.
Update. Here is Locke's exact quote where he denies Christ's satisfaction for sin:
If you will have the Truth of it, Sir, there is not any such Word in any one of the Epistles, or other Books of the New Testament, in my Bible, as Satisfying or Satisfaction made by our Saviour, and so I could not put it into my Christianity as delivered in the Scripture. If mine be not a true Bible, I desire you to furnish me with one that is more Orthodox; or if the Translators have bid that main Article of the Christian. Religion, they are the Betrayers of Christianity, and Condemners of the Epistles, who did not put it there; and not I, who did not take a Word from thence, which they did not put there. For truly, I am not a Maker of Creeds; nor dare add either to the Scripture, or to the Fundamental Articles of the Christian Religion.