Note that Madison, more than 200 years ago, viewed the morality as something separate from religion, exactly the opposite to what the "Corporate America Invented Christian America" promoters would expect us to believe now. And Madison writing so in not an accident -- it's a direct consequence of the ideas of Enlightenment which he accepted:
"Madison's ideas on philosophy and morality were strongly shaped by Witherspoon, who converted him to the philosophy, values, and modes of thinking of the Age of Enlightenment. Biographer Terence Ball wrote that at Princeton, Madison
was immersed in the liberalism of the Enlightenment, and converted to eighteenth-century political radicalism. From then on James Madison's theories would advance the rights of happiness of man, and his most active efforts would serve devotedly the cause of civil and political liberty."
"Madison's ideas on philosophy and morality were strongly shaped by Witherspoon, who converted him to the philosophy, values, and modes of thinking of the Age of Enlightenment. Biographer Terence Ball wrote that at Princeton, Madison
was immersed in the liberalism of the Enlightenment, and converted to eighteenth-century political radicalism. From then on James Madison's theories would advance the rights of happiness of man, and his most active efforts would serve devotedly the cause of civil and political liberty."
https://en.wikipedia.org/wiki/James_Madison
Ideas of Enlightenment and humanism are exactly the opposite of what the "corporate Christian" ideologists would like to sell everybody today.
Regarding the use of "religious" influence for political purposes, I also recommend the book:
https://www.amazon.com/Power-Worshippers-Dangerous-Religious...