I think far too much energy is being wasted by non-Christians in trying to prove that none of our Founder were Christian. I don't know where you got such a notion unless it comes from the all too common worldview of many who call themselves 'conservative, an attitude that says there are only two sides to every point of contention when in reality there is a spectrum of views. Some of the Founders were solid Christian believers, some were deists and there were some who saw religion as necessary, not because they personally believed in it but because they saw it as essential to control the lower classes "baser nature"
What's the point? The "point" is an attempt to show others that the rather simplistic view of the Founding Fathers that is promoted by far too many preacher-types is just a bunch of crap
Well it makes them feel good about themselves I suppose. Even a deist is a far cry from an atheist, or Buddhist or Hinduist, or a believer in relativism. I don't think there is any doubt, but more stubborness, in the minds of these people about whether this country was more Christian than anything else. The fact that they formed a "secular" government only means that there was enough respect for individual liberty and enough diversity in even the Christian sects, that they considered freedom of religion paramount. Well duh, the Founding Fathers had much more personal experience with the degree of animosity between the various Christian faiths than most modern Americans can understand. The basic point of Jefferson's letter to the Danbury Baptists was to emphasize that the new Constitution meant the Baptists would no longer be forced to support the Connecticut state church. This was the situation in several of the 13 states, where there was a state church supported by taxes paid by all citizens.
Remember that many early settlers came here to escape England's Church which was Christian. So our founders being Christians can most certainly go hand in hand with the formation of a secular govt. True and the Founders had personal knowledge of the animosity between the various Christian beliefs. The Puritans, so called because they were "Pure Christians", were amongst the most bigoted against those who did not belong to their church, they executed Quakers and Baptists who entered Massachusetts. This policy of intolerance led one of their ministers to leave Massachusetts and move to what is now Rhode Island to establish a more tolerant settlement.
And yes the Enlightenment had it's own level of influence, no doubt about it. But the American culture was long established before the Enlightenment made its way over here. Modern Americans find it difficult to understand just how much separation existed within colonial society, and early America too, between those we may call the landed gentry and the majority of the white population - nevermind the gap that existed between those of European descent and those from Africa and First Nations people. Almost all of the Founders would have been considered upper class, university educated folk, who had very different life experiences from most citizens.
As to the topic, no legal religious test is allowed for holding office. Many of the state constitutions were in place prior to the federal one, and at the time the founders were not going to try and dictate to the states on their internal affairs.