We argue over the heritage terms used to describe the American Founding -- "Christian," "Protestant Christian," "Judeo-Christian," "Theist," "Deist," "Unitarian," "Universalist," "Enlightenment," etc. America's Founders certainly well drew from the "Western" tradition. Is that synonymous with Christendom? Perhaps; but Western Civilization had a noble pagan Greco-Roman source as well which was certainly evident in the American Founding.
Terming the Founders as "Westerners" isn't to take a side in the culture wars that pits the defenders of Western Civilization against multiculturalism. Indeed, Multiculturalism itself is a Western concept. As is Marxism, classical liberalism and modern lefty liberalism and a whole bunch of other good and bad things.
Speaking of bad things, pagan Anglo-Saxonism, apart from fantasy literature and entertainment, really isn't respectable anymore, for obvious reasons (i.e., 20th Century German nationalism's poisoning its well). Yet, pagan Anglo-Saxonism represents another "heritage" source for Western Civ., though, the Anglo-Saxons weren't quite as accomplished as the Greco-Romans. Thursday is Thor's Day, after all.
What brings this to mind are the proposals for the Great Seal by Ben Franklin, John Adams and Thomas Jefferson. They proposed three different illustrative concepts: One, Moses and Pharaoh; two, Hercules "contemplating images of Virtue and Sloth"; and three, "Hengist and Horsa, the Saxon chiefs from whom we claim the honor of being descended, and whose political principles and form of government we have assumed."
Those three concepts include the Judeo-Christian, but also the pagan Anglo-Saxon and Greco-Roman.
Finally see historian Wayne Dynes' deconstruction of Jefferson's Hengist and Horsa proposal. As alluded to above, modern 20th-21st Century folks can get away with affinities for pagan Greco-Romanism, but pagan Anglo-Saxonism seems racist.
Update: Here is a link to John Adams' original letter.