The founding fathers were for a Republic.
They were against democracy except in some limited form.
The difference is fundamental .
Today ,they would ruefully remark they were prescient indeed.
The United States was far from a democracy until the 1920s.
They even avoided using the word.
Some of the radicals such as Jefferson did believe in greater element of democracy . but he was strongly opposed even more than many of the others to any inclusion of women, blacks, and .. big cities which he termed “ulcers on the body politic”.
They were also opposed to a “secular” entity.
Cf. Franklin’s quote of psalm 127:1
All of that came of age only in the 1920’s with womens’ vote and Jewish influence.
Furthermore ,they were aware that religion was meaningless unless it was hand in hand with moral character and patriarchal system