Those are not the Constitution RNR. That letter shows Jefferson's views. Jefferson did not attend the original CC. He was a deist and he referred to a Creator in his Dec, as to where rights came from. That was a public policy document justifying our secession from Britain.
My only point is that there is NOT a hard line. No one is compelled to believe in any religion. Some religious words here and there such as on coins are not a violation. Even the Constitution closes with the word "Lord" capital letters. Neither establish a church.
“Experience should teach us to be most on our guard to protect liberty when the Government’s purposes are beneficent. Men born to freedom are naturally alert to repel invasion of their liberty by evil-minded rulers. The greatest dangers to liberty lurk in insidious encroachment by men of zeal, well-meaning but without understanding.” — James Madison