Thomas Paine boldly self identified as a Deist and described his faith.
Every person, of whatever religious denomination he may be, is a DEIST in the first article of his Creed. Deism, from the Latin word Deus, God, is the belief of a God, and this belief is the first article of every man's creed. It is on this article, universally consented to by all mankind, that the Deist builds his church, and here he rests. ...Paine goes on. You can read the whole thing. But "and here he rests" draws a clear stopping line. His creed really was that simple. But what Paine noted in the above passage that EVERY PERSON of WHATEVER RELIGION believes in the "deistic minimum" is what the purveyors of natural theology believed.
Deists believed in "natural religion" only. Some orthodox Christians believe in natural religion (in the tradition of Aquinas et al.); some don't. But orthodox Christians (obviously) believe in biblical revelation too. Dr. Gregg Frazer's "theistic rationalists" too believed both in natural and revealed religion; but Frazer argues, they made revealed religion the handmaiden to natural religion.
One thing the "theistic rationalists" did often was speak in generic philosophical language of God (they were theological uniters, not dividers). One of their favorite ways to describe God was as a Being of infinite Wisdom, Goodness, and Power. (I'm surprised such language didn't find its way into the Declaration of Independence). Now, some orthodox Christians may also describe God using these three descriptors. In fact, they may have done it first. But the Deists too comfortably used that language. At least Thomas Paine did:
Its creed is pure, and sublimely simple. It believes in God, and there it rests.
It honors reason as the choicest gift of God to man, and the faculty by which he is enabled to contemplate the power, wisdom and goodness of the Creator displayed in the creation; ... [Bold mine.]As alluded to above, the purveyors of natural religion believed most all, if not all "religious" people worshipped the One True God of Wisdom, Goodness, and Power. Thomas Paine claimed to worship this God. The key Founders' language is replete with this exact reference to such God. John Adams claimed the Hindu Shastra teaches the existence and worship of such God, the very same God he claimed to worship.
Do all world religions really believe in the same One God of Wisdom, Goodness and Power? Who is this God?
Those are rhetorical questions, above my "pay grade" at the present moment.