The letter John Adams wrote is as clear as it can be. It unmistakeably says that the "Government of the United States of America is not, in any sense, founded on the Christian religion".
In other words, the Government of the United States is not a theocratic government; it is not influenced by or based on, or promoting Christian (or any other) religion because this country was not implicity or explciitly defined as a Christian nation in the Declaration of Independence, nor is her Constitution in any way, shape or form identified with any religion or deity.
The letter which Adams wrote to the Moslem was a diplomatic document, that is, he was LYING for his country, like any good diplomat.
Kosta is explicitly correct here. When America behaves as a theocracy is when it falters. See the current group of theocrats in the WH & Congress enforcing their beliefs on the nation.
That America was founded at all, most certainly came about because it was Christian and founded by Christians on Christian ideals.
Among all the nations of the world and across every religion in the world there is no other "America", no other bastion of liberty. Maybe Hong Kong comes close. That's proof enough that Christianity, along with the grace of God made the difference here.