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That can't be it, gentlemen.
The only part of the U.S. settled primarily by people fleeing religious persecution were the New England states, which are among the most irreligious in the U.S., and to some extent places like Pennsylvania (Quakers, who barely exist any more, and the ones who exist are extremely liberal), and Maryland (Catholics for the most part, and there weren't very many of them).
The only exception would be Utah, settled by persecuted Mormons.
The southern states were settled by people predominantly of the established religion, and they came for economic reasons, political persecution (Jacobites from Scotland), poor Brits from the Borders, because they were indentured servants, or criminals (Georgia, which was a penal colony like Australia).
The Baptists and Methodists, who had a very small presence in the south originally, exploded in terms of numbers after the Second Great Revival (there were three of them). Preachers from New England toured the south holding large meetings. The "revival" has a long history in the U.S.
https://en.wikipedia.org/wiki/Second_Great_Awakening
As for why it lingered longer, part of it may be that there has been less immigration to the southern states. They're not confronted as much with different points of view. It's also become part of their identity.
Southerners are more conservative altogether, not just in terms of religion. They're more patriotic, make up a very disproportionately large percentage of the armed forces.
Even in terms of manners, they're much more old-fashioned imo, more deferential to their parents, their elders, address people as ma'am or sir. It's a whole constellation of behavior.
Non si fa il proprio dovere perchè qualcuno ci dica grazie, lo si fa per principio, per se stessi, per la propria dignità . Oriana Fallaci