The history of our immigrants is a major part of the issue, certainly. Now, not all of the early immigrants left for religious reasons; Jamestown was unabashedly a commercial enterprise with a thin gloss of religious sentiment. However, several colonies were founded for specifically religious reasons. (Let me stick in a recommendation for Sarah Vowell's The Wordy Shipmates, which is a pretty good description of the religious nature of the early New England colonies.) Even when that reason was "because the colony next door is oppressing us," there was still sometimes the unmentioned "and we'd like to oppress other people instead."
This is probably part of why few listings of Presidents by religion ever have the word "deist," even when it's probably the best description. George Washington seems to have been a member of a church mostly because it was the socially correct thing to do at the time. Some Baptist congregation, I forget where, published a statement saying that it was better to vote for Jefferson than Adams, because the atheist probably wouldn't oppress them, and the Episcopalian might. Ben Franklin proposed (no one seems sure how seriously) that sessions of the Constitutional Convention begin with a prayer. The proposal was literally weeks into the convention and was never actually voted on, in part because they figured it would make it look to outside observers as though they were so stuck they needed divine assistance to form a working government.
