As the Government of the United States of America is not, in any sense, founded on the Christian religion; as it has in itself no character of enmity against the laws, religion, or tranquillity, of Musselmen; and as the said States never have entered into any war or act of hostility against any Mehomitan nation, it is declared by the parties that no pretext arising from religious opinions shall ever produce an interruption of the harmony existing between the two countries." Thomas Jefferson, speaking of Virginia's Act of Religious Freedom
1) That's typically Jeffersonian deism.
2) The idea is suicidal and contrary to reason.
Our system of government is suitable to all religions which recognize the natural law as a basis for law. This excludes Mohammedans because of their Sharia law, which often contradicts the natural law in important ways.
You combined my quotes. The one you listed was a treaty signed by the President and approved by the US Senate, merely a decade after the Constitution was written.
Your "natural law" exemption appears nowhere in that document, so it's meaningless.
-Eric