I would agree with you, although I would have nuanced it.... 

But all citizens and newcomers, for better or worse, still have to deal with our natural or civic religion, our " one nation under God" Pledge, our "endowed by the Creator" reference in the Declaration of independence,  our currency's "In God we Trust," our presidents swearing in protocol -- on a Bible, whether Lincoln's or their family's bible, etc. To comprehend this requires some understanding (literacy?) of our civic religion. Most Americans like this religion because it manages things comfortably for all faith communities, for the state, and for the unaffiliated. 
And although Americans don't need this to practice good citizenship, few citizens get in the way of doing away with this religion because they realize they haven't much social or cultural momentum to gain doing so. Things are often what they seem in America.