I think the constitution says it all. "We the people....." The only reference to the Christians # 1 God is as a place-holder in time.
Our liberty is deeply tied to our faith.
Yes, it's tied to everyone being able to have the faith of their own choice, not just "you can choose any religion in any color, as long as it's Christianity"
But Christianity prevails. If our founders were not Christian...would the outcome have been the same?
Well different religions would probably have done things differently in some way or other. But had the US been Christian but Russian orthodox, it would have been different. A lot of what you're talking about has been the development of Europe from the Magna Carta in 1215. Was Christianity the main driving force of parliament in England trying to rest control from the Monarch? No, because such things happened everywhere. You look to the Ottoman Empire and they had freedoms for different religions, and different ethic groups too, taking power away from the Sultan. But Christianity played a part because religion was far more political back then than it is now. But Christianity developed in different directions. Had the US been Catholic mainly, it would have gone a completely different way too.
But the Founding Fathers wanted to stop what had been happening under the British king George III. That is that religion was forced on people. The whole point of the First Amendment was so that individuals could make that decision.
And now you're trying to twist history to make it look like the Founding Fathers wanted the US to force religion on people.