A good number of them were “Christian deists”, and Thomas Jefferson called himself Christian in the sense that he followed Christ’s teachings yet he didn’t believe in the supernatural aspects or that he was the son of god. He made his own bible by tearing out the supernatural parts and only left behind Christ’s sayings and certain narratives of him
A bit of an oversimplification, their lot was diverse, some of the colonies they established genuinely sought religious freedom, like Rhode Island, while others were restricted to their puritan ideals, that contingent of them wanted to seek out a place for them and only them to practice their religion. By the time of the Declaration of Independence, many of the puritan’s descendants were more secularized in their disposition, ironically because of their emphasis on education.