[Matthew] Stewart is clearly arguing against claims of our modern religious right that the U.S. of A. was founded on and for Christian beliefs—almost always the beliefs of the people making those claims. As Stewart points out, people of a particular faith tend to assume that when historical figures they admire mention “God,” that means the same God they themselves believe in. But even when people of the past specifically allude to Christianity or Jesus, they may not share the same understanding of those terms and ideas as their modern readers.
That can cut in all directions. “Presbyterian“ was often used as a general derogatory term by eighteenth-century non-Presbyterians. John Adams’s understanding of “Unitarianism” doesn’t map directly onto the modern Unitarian-Universalist creed. And so on.