And those that had somewhat of a boot in each camp, still Christians but with a somewhat more material view of the value Christianity had, like John Adams and James Monroe.
Discussions about 'how Christian the Founders were' often comes down to how you view this last group, since they were (at least) nominally Christian, but they often separated the wisdom of Jesus, the importance of religious community in social terms, and the various miracles and supernatural claims of the Bible.
That last group is pretty broad if you compared Washington to Franklin, for example.
This is a useful point to remember as it creates a lot of eye of the beholder potential for the debate.
One issue with the group you describe is the concept of deism. Enlightenment era deists were mostly (although not uniformly) providential deists which is a bit different from the modern concept of deism.
A benevolent God created us with reason, wills human flourishing and has given us the tools to achieve this: the essential benevolence of creation can be decoded using reason. So for example Adam Smith considers the efficacy invisible hand of the market to be a function of Divine providence
This view developed out of Christianity and the idea we could return to a true 'natural religion' that is innate to us, as we transcended the need for revealed religion.
As the FF were mostly educated anglo-protestants, they subscribed to a whiggish view of historical progress, where basically the direction of history is for people to become more like them as they shed their superstitions and ignorance.
Where they stop on this process reflects the issue you describe: mainstream protestantism, providential deism or further towards atheism. It often didn't make a great deal of functional difference either.
Which gets to the problem with "Was America founded as a Christian nation?" because it is true to say both that it was and that it wasn't, or at least there is enough there for both sides to make a reasonable case in support of their position.
It was certainly founded on principles that emerged from the Christian tradition, although for numerous FFs these may have been understood as simply being universal truths. It wasn't founded as a religiously Christian nation though.
Many of the FFs were basically the Secular Humanists of the day: cultural Christians (well cultural anglo-Protestants) without the religious faith in Christianity. The benevolent god disappeared, but not the faith in the essential goodness of humans, and the explicit belief in Providence faded away over time, but is still just as powerful in contemporary Humanism rebranded as 'science and reason'.