Yeah, its not like the guiding principles of American Independence sprouted from perhaps the most irreligious period in European history since the completion of the Christian conversion...
The folks on the Mayflower sailed to the New World so that they could have it that their Puritanism would be the only faith. They were 'persecuted' in England for wanting to persecute. And let's not forget that the Mayflower was hardly the founding of America, coming over 120 years after the discovery of North America by Cabot, over 30 years after the naming of 'Virginia' and a generation after the founding of Jamestown.