The American Forefathers were inspired by Enlightenment philosophy, particularly by Classical Liberal thought. This means two things.

1. Most Enlightenment thinkers fought against superstition and supernatural understanding of everyday stuff. For example, Thomas Jefferson edited The Bible, to remove supernatural phenomena but to maintain the ethical teachings. What this means about their religious beliefs is that, if they believed in God at all, it was very different from how most people think about god. it was often impersonal, or a transcendental, not-so-relatable figure that was a symbol of perfection. It was not necessarily something to be pious toward or to worship.

2. This is the Classical Liberal part. They espoused the importance of forebearance rights, or rights not to do something (e.g. we have a right not to be killed, not to have our property stolen, etc.). They defined rights in these terms because it does not build beliefs into your norms. (If you think a government gives a right to a good standard of living, then the government has to define what "good" means, and often, that involves importing cultural biases about what "the good life" is.) By using a negative conception of rights, they understood it as being open toward many religions. By separating the church and the state, they understood that people could live while tolerating one another. Because there is a mutual agreement not to kill each other or to steal from each other, but because you're not concerned about telling people how to live their lives in substantive ways, you have a set of rules that allows you to live how you want (if you're not harming anyone), which allows society to be pluralistic.