I'll give it one more round. Just call me Mr. Quiote, thankyouverymuch.
Oversimplification.
The US wasn't founded on "strong religious sentiments". It was, in part, founded to insulate the Government from "strong religious sentiments". Actually, it was more part of the overall theme of avoiding entanglements. To follow a religion means, at least to a Western way of thinking, pledging feality to a higher being of some sort. This means that the government may not always hold its citizens' best interests in "mind".
Did the US FFs intend that everone who held public office be agnostic or atheist? No. No religious test, at all, is permissible by the US Constitution (or the preceding Articles of Confederation). This tells me that religion is not to be a litmus test, of any kind, for choosing political office holders. Granted, it's unreasonable to assume that voters wouldn't take the religon of the office-seeker in mind when they go to vote, but it should not be a de facto disqualifier.
Even today, there is no Official Religion of These United States. Faith-Based or no Faith Based. There is a predominant one. And it's the same, titualrly, that existed in 1782, that is Christianity. Let's face it, at the end of his life, Johnny Adams was concerned that Thomas Jefferson wasn't "right with God" and kept pestering TJ to accept Calvinism. Johnny was a Deist, earlier on, yet from Jefferson's writing you get the distinct impression that Adams had converted. We've had Episcopal (Anglican), Unitarian, Methodist and Quaker (did you know that Nixon was the US's last Quaker Prez?) presidents. Hell, even a Catholic snuck in for about three years. Would it be nice to get more diversity, yes. Should that be the only deciding factor? No.