Over at Claremont, Gregg Frazer reviews a book by Alf J. Mapp, investigating the faith of our founders. The book and its review seem to focus, certainly not on the beliefs of all of them, but rather on the central group of framers that includes the first four Presidents and the majority of those on the drafting board of the Declaration of Independence. We are talking about men like Washington, Adams, Jefferson, Madison, Franklin and a few others.
While I would make many points clarifying the following passage, I think, Frazer hits pretty close to the "natural religion" of our Framers (this natural religion is important because, its God, Nature's God, ultimately was the one who granted us our natural rights):
Although affiliated with various denominations, the major founders did not typically hold to the beliefs officially espoused by their denominations. Similarly, while Franklin and Jefferson are regularly listed as deists, they did not believe in the fundamental tenets of deism. The key founders shared a common belief which might be called theistic rationalism. Theistic rationalism was a hybrid, mixing elements of natural religion, Christianity, and rationalism, with rationalism as the predominant element. Accordingly, the founders believed in a benevolent, active, and unitary God who intervenes in human affairs. Consequently, they believed that prayers are heard and effectual. They believed that the key factor in serving God is living a good and moral life, that promotion of morality is central to the value of religion, and that the morality engendered by religion is indispensable to society. Because virtually all religions promote morality, they believed that most religious traditions are valid and lead to the same God.
Though theistic rationalists did not believe that Jesus was God, they considered him a great moral teacher and held a higher view of him than did deists. They believed in a personal after-life in which the wicked will be temporarily punished and the good experience happiness forever. Although they believed that God primarily revealed himself through nature, they believed that some written revelation was legitimate. Finally, while they believed that reason and revelation generally agree with each other, theistic rationalists believed that revelation was designed to complement reason (not vice versa). Reason was the ultimate standard for learning and evaluating truth and for determining legitimate revelation from God.
First off, when Frazer writes that Franklin and Jefferson rejected "the fundamental tenets of deism" he is referring to the tenet of deism that posits a strictly non-interventionist Deity and that both of these men alluded to a Providence that intervened. Moreover, Frazer notes (before the above passage) that Jefferson never claimed to be a deist. That is wrong. Jefferson did claim to be a deist, and a unitarian, and a Christian.
Regarding deism and interventionism, it depends on how one defines "deism"; yes there was a strand of strict capital D Deism that posited a God that absolutely did not intervene. And very few of our founders fit this definition. However, there is a broader understanding of deism as well. As Russell Kirk wrote in Roots of the American Order:
Deism was neither a Christian schism nor a systematic philosophy, but rather a way of looking at the human condition; the men called Deists differed among themselves on many points. Deism was an outgrowth of seventeenth- and eighteenth-century scientific speculation. The Deist professed belief in a single Supreme Being, but rejected a large part of Christian doctrine. Follow Nature, said the Deists (as the Stoics had said before them), not Revelation: all things must be tested by private rational judgment.
This seems to be entirely consistent with what Frazer terms, "theistic rationalism." I'm not sure what to call it: deism, unitarianism, theistic rationalism, but it seems to be the baseline of our founders' natural religion that dovetails with our founding political principles or "the laws of nature and nature's God."
One other thing, about God's interventionism: Jefferson did indeed write about society feeling God's wrath if we didn't respect natural rights. And Washington and others spoke about God's Hand of Providence guiding human affairs. However, as rationalists, they were extremely skeptical about miracles. Jefferson believed most, if not all of the miracles of the Bible to be fiction. So when God did intervene he didn't do so by parting the Red Sea or Walking on Water. He did so by acting in accordance with the rules of science, not by breaking them. For instance, "We miraculously won such and such a battle against the British"; that could be God's work. But what God didn't do was send any magical lighting bolts or do a magic act that contradicts the laws of nature in our favor.