Perhaps it's because of the congregationalist nature of most Puritan churches? The fact that towns could change their local church rules according to societal whims meant that not only could the prevailing ideology change with relative ease without the mandates or diktats that we see in other ecclesiastical structures, but also meant there was no need to search for another upstart religion to join.
And this same dynamic also worked in the opposite direction of “secular and socially liberal” outside of New England - most dramatically in the South, which of course has a very different social, economic, cultural, and demographic history than New England.
I agree with Averroes that Catholicism is underrated as a factor here, especially considering how Catholics were historically among the “outs” of Protestant-dominated American society. Yet many of the descendants of working-class Catholic immigrants are thoroughly assimilated and highly educated, urban professionals. Secular and socially liberal, indeed.
I would also note how
old New England is; how, from very early on, it’s had a strong tradition of local government, civic participation, and yes, obviously education (and this is directly a product of New England religion; note who the Ivy League colleges were founded by...).
Another thing is geography. New England is
small, coastal or close to the coast (many major ports with long histories), and with cities, towns, and neighborhoods that tend to be more like Europe than to the suburban sprawl of much of the rest of the USA.
All of this is at least related to the answer(s) to Scott’s question, if not causal factors in and of themselves.