But the widespread existence in 18th-century America of a school of religious thought called Deism complicates the actual beliefs of the Founders. Drawing from the scientific and philosophical work of such figures as Jean-Jacques Rousseau, Isaac Newton, and John Locke, Deists argued that human experience and rationality—rather than religious dogma and mystery—determine the validity of human beliefs. In his widely read The Age of Reason, Thomas Paine, the principal American exponent of Deism, called Christianity “a fable.” Paine, the protégé of Benjamin Franklin, denied “that the Almighty ever did communicate anything to man, by…speech,…language, or…vision.” Postulating a distant deity whom he called “Nature’s God” (a term also used in the Declaration of Independence), Paine declared in a “profession of faith”:

Thus, Deism inevitably subverted orthodox Christianity. Persons influenced by the movement had little reason to read the Bible, to pray, to attend church, or to participate in such rites as baptism, Holy Communion, and the laying on of hands (confirmation) by bishops. With the notable exceptions of Abigail Adams and Dolley Madison, Deism seems to have had little effect on women. For example, Martha Washington, the daughters of Thomas Jefferson, and Elizabeth Kortright Monroe and her daughters seem to have held orthodox Christian beliefs.
http://www.britannica.com/topic/The-Founding-Fathers-Deism-and-Christianity-1272214

But the widespread existence in 18th-century America of a school of religious thought called Deism complicates the actual beliefs of the Founders. Drawing from the scientific and philosophical work of such figures as Jean-Jacques Rousseau, Isaac Newton, and John Locke, Deists argued that human experience and rationality—rather than religious dogma and mystery—determine the validity of human beliefs. In his widely read The Age of Reason, Thomas Paine, the principal American exponent of Deism, called Christianity “a fable.” Paine, the protégé of Benjamin Franklin, denied “that the Almighty ever did communicate anything to man, by…speech,…language, or…vision.” Postulating a distant deity whom he called “Nature’s God” (a term also used in the Declaration of Independence), Paine declared in a “profession of faith”:

Thus, Deism inevitably subverted orthodox Christianity. Persons influenced by the movement had little reason to read the Bible, to pray, to attend church, or to participate in such rites as baptism, Holy Communion, and the laying on of hands (confirmation) by bishops. With the notable exceptions of Abigail Adams and Dolley Madison, Deism seems to have had little effect on women. For example, Martha Washington, the daughters of Thomas Jefferson, and Elizabeth Kortright Monroe and her daughters seem to have held orthodox Christian beliefs.
http://www.britannica.com/topic/The-Founding-Fathers-Deism-and-Christianity-1272214

Many Founders who were what was known as "anti-clerical Christians" were mistakenly called Deists. There were 55 delegates at the original Constitutional Convention. Forty-nine identified as some denomination of Protestant Christian, with a couple of Catholics and others thrown in.
In the 17th and 18th centuries, religion, in the form of the Roman Catholic Church of France and Spain, and, to a lesser degree the Church of England were in fact a branch of government. They were far more secular than spiritual at least among the higher ups. The First Amendment prohibition against making any law regarding the establishment of religion or the free exercise thereof was to prevent a pseudo-Theocracy such as existed in Spain especially from taking root in the US.
Anti-clerical Christians were Christians who eschewed the trappings of organized religion, and ordained clergy. They were often mistakenly identified as Deists.