In his book Education: Free & Compulsory, Rothbard says that education in the South was mostly private, except for some public schools for the poor. The North, particularly Massachusetts, had public schools for everyone with compulsory laws. They were run by the Puritans, so they were Christian at the time. The compulsory laws were interrupted by the Revolutionary War, but they picked back up again in the mid 1800s. This model then spread through the rest of the country.
Virginia, typically of southern states, didn’t have public primary and secondary education until Reconstruction. The best estimate is that about half of Virginian white men were illiterate at the time of the Revolution. Jefferson proposed extensive reforms in this area, which are the subject of one chapter of my forthcoming book, Thomas Jefferson–Revolutionary.