I think I know some of the things that the ACTUAL founding fathers thought about the value of religion in politics.....because they actually said them..
And while they were Christian, they certainly give me them impression that the role of god in government was ziltch.

"While we are zealously performing the duties of good citizens and soldiers, we certainly ought not to be inattentive to the higher duties of religion. To the distinguished character of Patriot, it should be our highest glory to add the more distinguished character of Christian."

--The Writings of Washington,

"The general principles on which the fathers achieved independence were the general principles of Christianity. I will avow that I then believed, and now believe, that those general principles of Christianity are as eternal and immutable as the existence and attributes of God."

--Adams wrote this on June 28, 1813, in a letter to Thomas Jefferson.

"God who gave us life gave us liberty. And can the liberties of a nation be thought secure when we have removed their only firm basis, a conviction in the minds of the people that these liberties are of the Gift of God?"

--Thomas Jefferson, Notes on the State of Virginia, Query XVIII, p. 237.

"Cursed be all that learning that is contrary to the cross of Christ."

--James Madison, America's Providential History, p. 93.

"When we view the blessings with which our country has been favored, those which we now enjoy, and the means which we possess of handing them down unimpaired to our latest posterity, our attention is irresistibly drawn to the source from whence they flow. Let us then, unite in offering our most grateful acknowledgements for these blessings to the Divine Author of All Good."

--James Monroe made this statement in his 2nd Annual Message to Congress, November 16, 1818.

"The hope of a Christian is inseparable from his faith. Whoever believes in the divine inspiration of the Holy Scriptures must hope that the religion of Jesus shall prevail throughout the earth."

--Life of John Quincy Adams, p. 248.

"I have carefully examined the evidences of the Christian religion, and if I was sitting as a juror upon its authenticity I would unhesitatingly give my verdict in its favor. I can prove its truth as clearly as any proposition ever submitted to the mind of man."

--Alexander Hamilton, Famous American Statesmen, p. 126.