First and foremost, there's the ban on all religious tests for office – a clear sign of the influence of the Enlightenment and a stark departure from previous norms – right there in Article VI of the Constitution: "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States."
Second, and more important in the public mind for centuries, was the twinned statements in the First Amendment that "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof."
That's it. That's all the religion in the Constitution: No religious test for office holders; the state they led couldn't force a national religion on its people; the people were free to worship however they wanted.
In case that wasn't clear, the federal government spelled it out clearly in the Treaty of Tripoli. A document begun by Washington, signed by Adams, and ratified by a Senate whose membership was half-filled with ratifiers of the Constitution, the Treaty puts it in plain English for anyone who missed it: "the government of the United States of America is not in any sense founded on the Christian Religion."
So when these people talk about "rededicating" the USA to its rightful place as "one nation under God," remember that they have no legitimate claim. The politics they're trying clumsily to recreate comes not from the founding fathers in the 1770s, but from the era of our grandfathers and great-grandfathers in the 1950s.
But, again, as I noted in the book, even that era's religious nationalism was not narrowly focused on Christianity in general (or evangelical Protestantism in particular as this group is).
There were numerous expressions of religious nationalism in the 1950s – ranging from the addition of "under God" to the Pledge and the adoption of "In God We Trust" as the national motto to events like the National Prayer Breakfast – but these expressions were always drawn broadly. They invoked God, but never Jesus.
It was an approach, as Yale Law School Dean Eugene Rostow put it, marked by "ceremonial deism." The deity was always drawn as broadly as possible, so that Protestants, Catholics and Jews could all find meaning in it, but also Muslims, Hindus and Buddhists. (The only ones outside the circle were American atheists, whom President Dwight Eisenhower once called "a contradiction in terms.")
Unlike the Trump era, where expressions of sharp-elbowed evangelical Christianity dominate the discourse, the religious nationalists of the Eisenhower era were much more circumspect about foregrounding Christianity this much.