That was the ground of the perpetuation of religious establishment in the Massachusetts Constitution of 1780: a good society required a moral people; average people wouldn’t be moral absent belief in a future state of rewards and punishments; belief in a future state of rewards and punishments came from religion; in order for all to be religious, they must be made to participate; Massachusetts residents weren’t going to be Catholic, Muslim, or Episcopalian; so the Congregationalist Establishment must continue.
Ben Franklin, not a religious man, famously said that he would not want to live in a non-Christian society because Christians made good neighbors.
Nowadays we tend to think of Christianity’s moral residue in our culture as somehow neutrally derived. Yet, monogamy, private property, and various other of our conventions are specific to our culture, where (like St. Constantine’s bans on infanticide and crucifixion and institution of the Sunday holiday) they have their origins in Christianity. I think we can see the post-Enlightenment history of the West as a long experiment to see whether decency can survive the decline of its source.