This isn't true at all. The article in the Amendment is a specific injunction that Congress not establish an official religion for the United States. The Founding Fathers fully expected religion, specifically sects of Christianity, to play a prominent social and moral role in every aspect of lives of their new countrymen. The purpose of the specific rejoinder of not establishing one official religion wasn't to prevent religion from affecting politics but to protect the expression of all religions in public life since the role of religion across the board was a given. That religion would have a seminal role... one so important that expression of it had to be protected... was a basic presumption by the Founding Fathers.
Keep in mind that Americans generally see the Constitution as the moral foundation of our nation... for example people will argue that Free Speech is an imperative because Free Speech is protected in the Bill of Rights. Likewise people will argue that it's a moral right to bear arms because the Amendments to the Constitution protect the right to bear arms.
The Founding Fathers themselves derived no moral authority from the Constitution... they were the ones who wrote it... and the principles they wrote into the Constitution were almost exclusively drawn from the morality they derived from Christianity... for example individual liberty and equal rights in the Constitution are valid because of the Christian concept of Man's equality under the eyes of God etc. Individual values and judgments on what's "right" weren't derived from the Constitution but the other way around. What their religions and philosophy taught them was codified into the provisions of the Constitution.
Bottom line is that the modern idea that the Constitution somehow limits the role of religion in public life is just nonsense. The protection wasn't originally created that religion be limited in its influence in public life but that the expression of all religion be equally protected. I am an atheist FWIW.
