Most of them, at least the ones most responsible for drafting the Constitution, were deists, as was common for intellectuals during the Enlightenment. Jefferson, Madison, Franklin and Monroe were all deists. They generally accepted that Jesus existed and he brought great wisdom of the world but they also questioned his divinity. And even the professed Christians, like Adams, were heavily influenced by progressive Unitarian principles, which did not believe in religious supremacy over government.
Jefferson was so unconvinced of Christ’s divinity that he edited the New Testament down to what he considered to be the wisdom and took out all of the supernatural elements.