So, for instance, America's key Founders, following natural religion, held all religious men of all of the worlds' religions worshipped the same God, wherein they argue over the details. Indeed, the knowledge that such a God exists without any external written revelation is available to all men through the use of reason and the senses.
As it were, it's not just Jews, Christians and Muslims who worship this same One True God, but so too do unconverted Native Americans (they call Him "The Great Spirit") and Hindus (as the Founders would say "Hindoos"), just about everyone.
Over the years, I have presented these findings to folks who read it with a very skeptical eye. They don't like how America's "Christian" and "Judeo-Christian" contributions have been, as they see it, sandblasted from the public square. So they seek to reauthenticate for traditional Christianity what is presented as a novel creation of the Enlightenment period.
So I have been told the idea of natural religion, (again, the notion that all men, through the use of reason alone can know God exists and thus worship the same God while differing over the details) has been and is believed in by bona fide historic orthodox Christians. And though they don't all believe it, such is something consistent with the traditional practice of the faith.
America's Founders certainly had an ecumenical impulse that the natural law-natural religion satisfied. On the other hand, there is and always has been an anti-ecumenical impulse. The idea that we've got the details all right and you've got it all wrong. Hence your god is/gods are false. America's Founders, for the most part, rejected such.
(The concept of puritanism or separating and purifying the true practice of the faith from the false represents such anti-ecumenism. And this doesn't always produce bad results. Roger Williams' good results on religious liberty were significantly driven by such.)
Even for Young Earth Creationist believing fundamentalists, natural religion might provide some kind of rational explanation, given their premises: If God created Adam and Eve and all humanity is so derived, and given most history, especially from very early on, is transmitted orally, it makes sense that those who best kept the faith would have the clearest details of what's true, but that everyone still has some key details right, even if distorted, because we all come from the same place.
If all world religions worship the same God, then how do we deal with the issue of polytheism v. monotheism? First, it's not clear that "the monotheistic religions" are as monotheistic as they present themselves. Just as it's not clear that the polytheistic religions are as polytheistic as they have been purported to be.
The Bible doesn't simply speak of the One God in the heavenly realm and the many of humanity. Rather, from the beginning it seems there exists a divine heavenly family. Mormons, for instance, have been characterized as polytheistic. To which they accurately reply no, they are henotheistic. Indeed, it's debatable whether the Bible teaches monotheism or henotheism.
Small o orthodox Christianity teaches the existence of One God who exists in Three Eternally Distinct Persons. This gets them a charge of polytheism from, among others, Muslims.
It's the idea of the More Than One deriving, in some mysterious way, from The One. Again, it's not some fuzzy New Age concept, but an issue that has long perplexed metaphysicians and philosophers.
So Hinduism has countless gods (perhaps the most) in its pantheon. But Hinduism can and certain forms do argue the religion is actually monotheistic in that all of the different gods are manifestations of the One True God. Hindus also have a Trinity that parallels the Christian One: It's Brahma, Vishnu, and Shiva. Now, someone committed to an anti-ecumenical understanding of orthodox Christianity, might argue such Trinity has nothing to do with the Christian Trinity.
But that's not what John Adams thought. As he wrote to Thomas Jefferson, December 25, 1813:
Where is to be found theology more orthodox, or philosophy more profound, than in the introduction to the Shasta? "God is one, creator of all, universal sphere, without beginning, without end. God governs all the creation by a general providence, resulting from his eternal designs. Search not the essence and the nature of the Eternal, who is one; your research will be vain and presumptuous. It is enough, that, day by day and night by night, you adore his power, his wisdom, and his goodness, in his works. The Eternal willed, in the fulness of time, to communicate of his essence and of his splendor, to beings capable of perceiving it. They as yet existed not. The Eternal willed, and they were. He created Birma, Vitsnow, and Sib." These doctrines, sublime, if ever there were any sublime, Pythagoras learned in India, and taught them to Zaleucus and his other disciples.Now, the militant unitarian John Adams devoutly believed in the One True God of the Universe. But he bitterly rejected the orthodox Christian doctrine of the Trinity. The overall context of his letter was to both 1. endorse the natural religion notion that all of the world religions worship the same God, even as they differ over the details, and 2. articulate the genealogy of the Christian Trinity which he rejected as false. Enlightenment rationalists who rejected the Trinity tended to blame Plato for the "fabrication" of the doctrine. But Adams in this letter traces it to Pythagoras.
Adams believed both the Hindu and the Christian understandings of the Trinity have the same origin. This too could be understood as a function of natural religion, that all world religions in their essence teach more or less the same thing, ascertainable by reason. But that using their reason, dicker on the exact details.
Indeed, the orthodox Christian American Founder Elias Boudinot recognized the similarity between the Christian and Hindu doctrines of the Trinity and likewise attempted to trace the genealogy of the doctrine. But unlike Adams, Boudinot accepted the Trinity as part of Christian doctrine. So, as it were, the Hindus must have got it from the Hebrews. As per the natural religion explanation, all world religions believe in the same essential truth, discernible from reason and the senses, even if the different groups distort details.
But still, what J. Adams and E. Boudinot would both agree with is that orthodox Christianity and Hinduism share the notion that from the One True God manifests Three. The Hindu notion is that there is One that splits into Three (and then perhaps more). The orthodox Christian notion is that from One, in some mysterious way, Three Exist.