IMO, The Founders of the United States were both Christian and deeply religious; however, I suspect they had a radically different understanding of religion than we have today.
The founders had a much more rational understanding of Christianity.
The founders had a classical education. The legs of the Trivium are language, logic and rhetoric. The classical tradition would have held that God is Truth and students would then cut their teeth applying logic to their cultural tradition.
A quality education would bring up questions about what is reason? What is truth, etc.? The classical liberal traditional proceeded along the line that there was One God, One Truth but that we all head different and woefully incomplete perspectives of the truth.
BTW: You don't need to be looking at something that is absolutely true to have a discussion about truth. Imagine that an orc and a hobbit were doing arithmetic. The orc says "2 + 2 = 4." Does the truth associated with the statement "2 + 2 = 4" change because orcs are fictional creatures?
I find that questions of truth are best discussed in context of the known instead of the unknown.
There are, of course, some ugly aspects of religion. There is a long history of rulers oppressing the people with religion. Politicians and rulers see religion as a tool for imposing authority. The last post brought up Robert Filmer who spat nonsense in defending the divine right of kings.
Interestingly, when the ruling class had finally worn out its theological justifications for its authoritarian rule, the ruling class turned to a radicalized form of anti-religion non-sense to justify authoritarian rule (Feuerbach, Marx, etc).
Modern dialectics (Hegel, Feuerbach, Marx) is a game in which one holds a paradox at the base of reason and conflict at the surface. Atheists holds the belief that they hold no belief (the reflexive paradox). Atheists of the Hegelian/Marxist tradition then construct a belief system based on eternal conflict. On reading the Black Book of Communism, one discovers that more people have been killed in the name of this new non-belief than traditional beliefs).
In my reading of the Founders, it appears that the Founders were deeply Christian. Their Christianity was wrapped up in a different rational style.
It is this rational style that we need to preserve. Sadly, I fear that many modern Christians have abandoned the rational tradition of Christianity for its base superstitions. Some modern sects seem to hold the God is a dancing clown who does magic. The primary goal of God is to give political authority to a chosen few... all outside the confines of that chosen few are servants of Satan.
I like the idea that God is Truth. Although much of the mythology of Christianity is suspect, I find within the traditional a beautiful rational style.
Holding that God is Truth, of course, puts one in conflict with those who invoke the name of God to establish political authority. Such sects hold that truth is what advances the political authority. It is a chain of thought that gets ugly, quickly.
Here behind the Zion Curtain, I've actually had people wearing white shirts and name tags call me Satan for rejecting the political hierarchy. It would be funny if it wasn't so sad. It is next to impossible to have a rational conversation with people who belief that those outside the political authority are Satan.
While waiting for a train a while back, I learned that the direction a train is facing tells me more about where the train is going than the history of where the train's been. If there is a train of people who are authentically engaged in a pursuit of truth, they are likely to go in a more promising direction than a train of people who are starting on solid ground but are heading off on a pursuit of power through conflict.
There was a beautiful rational style that emerged in the Western Christian tradition. It breaks my heart that the tradition has been taken over by a religious right who simply use Christianity in their pursuit of power and forget the time-honored tradition of the pursuit of truth.