To understand how it was in early America, one need look no further than the first American President:
I never witnessed his private devotions. I never inquired about them. I should have thought it the greatest heresy to doubt his firm belief in Christianity. His life, his writings, prove that he was a Christian. He was not one of those who act or pray, that they may be seen of men [Matthew 6:5]. He communed with his God in secret [Matthew 6:6].
Nelly Custis-Lewis, 1833, Granddaughter of Martha Washington
http://www.christiananswers.net/q-wall/wal-g011.html
And the Virginia Baptists along with John Leland by no means kept their faith in a closet (the un-Christian right now wants Christian right in a closet while okay-ing the sodomites to come out of the closet). They publicly pushed for the Bill of Rights in Philadelphia and obtained Madison’s ear.
Washington’s Chaplain during the Revolution was Baptist John Gano, who baptized Washington. Washington said, (almost verbatim) “The war is my separation with political England and my Baptism is my break with religious England.”
I recommend to you the books of historians Rosalie J. Slater and Dr. James Beller.
The truth still remains that America at its founding was overwhelmingly and predominantly Christian right. It would be insane to believe that that did not influence every area of life in the colonies/states, including its politics.
The founders made open and published statements in favor and support of the Bible and the teaching and learning of it.
This is an exhibition of the Library of Congress. It is shocking:
Religion and the Founding of the American Republic
http://www.loc.gov/exhibits/religion/