I would argue that the founding principles are not religious, but they are existential and not "humanist". JMHO.
There was a study done by political science professors at the University of Houston. They rightfully felt that they could determine the source of the Founders’ ideas if they could collect the writings from the Founding Era and see whom the Founders were quoting.
The researchers assembled 15,000 writings from the founding Era – no small sample – and searched those writings. That project spanned ten years; but at the end of that time, the researchers had isolated 3,154 direct quotes made by the Founders and had identified the source of those quotes.
The researchers discovered that Baron Charles de Montesquieu was the man quoted most often by the founding fathers, with 8.3 percent of the Founders’ quotes being taken from his writings. Sir William Blackstone was the second most-quoted individual with 7.9 percent of the Founder’s quotes, and John Locke was third with 2.9 percent.
Surprisingly, the researchers discovered that the founders quoted directly out of the bible 4 times more than they quoted Montesquieu, 4 times more often than they quoted Blackstone, and 12 times more often than they quoted John Locke. Thirty four percent of the Founders’ quotes came directly out of the bible.
The study was even more impressive when the source of the ideas used by Montesquieu, Blackstone, and Locke were identified. Consider for example, the source of Blackstone’s ideas. Blackstone’s Commentaries on the Laws was first introduced in 1768, and for the next 100 years America’s courts quoted Blackstone to settle disputes, to define words, and to examine procedure; Blackstone’s Commentaries were the final word in the Supreme Courts. So what was a significant source of Blackstone’s ideas? Perhaps the best answer to that question can be given through the life of Charles Finney.
Charles Finney is known as a famous revivalist, minister, and preacher from one of America’s greatest revivals; the Second Great Awakening in the early 1800’s. Finney, in his autobiography, spoke of how he received his call to ministry. He explained that – having determined to become a lawyer – he, like all other law students at the time, commenced the study of Blackstone’s Commentaries on the Laws. Finney observed that Blackstone’s Commentaries not only provided the laws, it also provided the Biblical concepts on which those laws were based. Finney explained that in the process of studying Blackstone, he read so much of the Bible that he became a Christian and received his call to the ministry. Finney’s life story clearly identified a major source of Blackstone’s ideas for law.
So, while 34% of the Founders’ quotes came directly out of the Bible, many of their quotes were taken from men – like Blackstone – who had used the Bible to arrive at their own conclusions.”
This doesn’t even include Supreme Court decisions, Congressional records, speeches, inaugurations, etc. all of which include sources of Biblical content and concepts.