Hart comes to many of the same discoveries and conclusions on religion and public life that I have (no wonder I like his address so much). An orthodox Calvinist, Hart makes the case that politically conservative Christians, especially Calvinists, should embrace some kind of secularism (which he defines as government neutrality towards religion) because America's Founding political theology does not resonate with orthodox Christianity. The political theology of the American Founding is especially in tension with Calvinism.
The bottom line is America's Founding political theology is a unitarian theology of works, not an orthodox theology of grace. Though he doesn't cite Franklin's quotation, the following perfectly exemplifies the way "religion" was meant to resonate with the republicanism of the American Founding:
Faith is recommended as a Means of producing Morality: Our Saviour was a Teacher of Morality or Virtue, and they that were deficient and desired to be taught, ought first to believe in him as an able and faithful Teacher. Thus Faith would be a Means of producing Morality, and Morality of Salvation. But that from such Faith alone Salvation may be expected, appears to me to be neither a Christian Doctrine nor a reasonable one….Morality or Virtue is the End, Faith only a Means to obtain that End: And if the End be obtained, it is no matter by what Means.
-- “Dialogue between Two Presbyterians,” April 10, 1735.
Though George Washington was never so explicitly heterodox (for pragmatic reasons) his Farewell Address is pregnant with heterodox unitarian implications as it well illustrates this unitarian-utilitarian theology of works, as opposed to an orthodox theology of grace:
Of all the dispositions and habits which lead to political prosperity, religion and morality are indispensable supports….And let us with caution indulge the supposition that morality can be maintained without religion. Whatever may be conceded to the influence of refined education on minds of peculiar structure, reason and experience both forbid us to expect that national morality can prevail in exclusion of religious principle.