Wood addresses the question in the first part of his book [Empire of Liberty (Oxford Univ. Press, 2009)], proposing that Masonry played a dual role as a source of unity in America and as a new religion designed to replace Christianity for those skeptical of Christianity's claims. His take on Masonry is set out on page 51 of the book:
Freemasonry was a surrogate religion for enlightened men suspicious of traditional Christianity. It offered ritual, mystery, and communality without the enthusiasm and sectarian bigotry of organized religion. But Masonry was not only an enlightened institution; with the Revolution, it became a republican one as well. As George Washington said, it was "a lodge for the virtues." As Masonic lodges had always been places where men who differed in everyday affairs -- politically, socially, even religiously -- could "all meet amicably, and converse sociably together." There in the lodges, the Masons told themselves, "we discover no estrangement of behavior, nor alienation of affection." Masonry had always sought unity and harmony in a society increasingly diverse and fragmented. It traditionally had prided itself on being, as one Mason put it, "the Center of Union and the means of conciliating friendship among men that might otherwise have remained at perpetual distance."