Really high concentration of college grads vs. nationwide. That's the bottom line. New England being relatively secular could be a small part of the story, but with Trump improving in places like Las Vegas, L.A. and South Florida, I think it's very overrated.
The common thread between all those places is they have a very large number of Hispanics; New England does not. That was a whole separate issue, and it has nothing to do with the fact that secularism is the most likely reason New England so sharply shifted away from Trump (even relative to trends we saw in other educated white areas), or the proven fact that religion is the single most reliable demographic predictor of how people vote. More than race, even. Unlike the Hispanics in the areas you mentioned, New Englanders are largely not just "secular;" they are actively irreligious, while most Hispanics are at least culturally Catholic even if they do not practice it devoutly. And being irreligious is the single strongest predictor of voting Democratic.