If God has been outlawed from American schools, it's because he always eventually tries to outlaw or suppress science, independent thought, and critical thought once you let him through the front gate. Christianity and a liberal education are mutually exclusive wherever they overlap. Pick one.
Likewise in government. If you don't keep religion out of democratic government, it will work tirelessly to take control and exterminate democracy. Yahweh is an autocrat and his government is a patriarchal, hierarchical dictatorship that acknowledges no rights.
America's prosperity has nothing to do with religion. It is rooted in its size, its wealth of natural resources, its relative isolation from Europe, and the fruits of scientists. And freedom, as alluded to above, is antithetical to the Judeo-Islamo-Christian model. Obedience, however, is not.
To what religious principles do you suppose that he referred? I am only aware of one principle common to all religion: have faith, that is, believe what you are told however little supporting evidence or how much contradictory evidence exists.
Even the principle that reality is radically different than it appears to be (such as that you are born a sinner in need of salvation) or that there are unseen aspects of reality (such as Hell and Satan), it is not of Christian origin, just the particular dogma. Plato taught that the unseen world is more real than the world of experience.
Maybe he meant Christian principles. If so, this is wrong too because our legal heritage is older than British Christianity and has roots in the Celtic common law. Plus, we have rejected Judeo-Christian laws such as honor the Sabbath or worship Yahweh and no other god.
The parts of our legal heritage that made America great for a time were novel then: limited and diffused governmental power and constitutionally guaranteed rights of individuals and minorities. What could be more antithetical to a Christian law than that? The last Christian government here precedes America, and it burned witches.
If by religious principles you mean don't kill your own and don't steal from your own, that is a principle that all healthy people discover and embrace without religion. Eventually, if they can overcome the divisiveness and violence resulting from their religions and other cultural segregators (national boundaries, languages), they can start to see all people as their own and extend the courtesy of honesty and nonviolence even to exotic strangers. I'm sure that even Attila, whatever his belief system, banned killing and stealing between his troops. Those are not religious principles.
Judeo-Islamo-Christian tradition has no problem with killing and stealing from strangers, beginning with the Promised Land and continuing right up to the invasion of Iraq. Don't be fooled by the empty platitudes that preachers sermonize about every Sunday or put up on the sign outside of the church for passers by to read. They don't represent what religion actually does or actually teaches by example, just to what it gives lip service.
Religious principles are peculiar to religion and include things such as the alleged power of prayer, the importance of getting baptized or the existence of angels. They have no meaning outside of particular religions. So, they are religious principles in Catholicism and for Baptists, but not for Muslims. None of these religious principles apart from the principle of faith in authority spans all the religions, and therefore none deserves the name religious principle just Christian principle or Baptist principle.
Faith (certainty without proof) is different from ordinary belief (probability based on past experience a or trusted source), and is antithetical to reason just as Christianity was just shown to be antithetical to democracy. Literally. Think about that for several minutes. Faith and reason cannot be applied at the same time to anything. They are like oil and water, but even more so. They are mutually exclusive. Faith based thinking is believing something that is not evidence based. Reason is nothing but. Otherwise, it's ordinary belief (expectation), not faith (certainty).