Jefferson was not a non-Christian (these are huge falsehoods), and neither were the men such as Adams and Franklin who helped tweak it, nor the other men on the committee Livingston and Sherman.
The founders were a mixed lot in terms of religious opinions, although few were of the orthodox/Calvinist variety. The second and third Great Awakenings, which came a few decades after the founding, were a much bigger factor in pushing Christian political activism to the forefront in national politics (although even in the revolution, there were large communities of "Christian activists" in support of the cause. See, the Baptists as a case in point).
I find it interesting that the GOP nominated a not-very-serious Quaker (!) as their candidate (Nixon), and a believing, but non-Churchgoing Christian as their candidate (Ronaldus Magnus), but it seems to me that such men would have difficulty being vetted by the Churchianists (notice I didn't say Christians).