In part, it has to do with the lower religiousness in the area, as well as different kind of religiousness compared to the midwest etc.
[New England] evolved into the most secular part of the country. In the words of one regional missions group, “pulpits that once boasted gospel preachers like Jonathan Edwards and George Whitefield now proclaim universalism, liberalism, and postmodernism.” A Gallup poll this year  found that the four least-religious states in America are in New England.
Of course, this is a bit of a "chicken and egg" problem, as one can then ask, what explains the latter trend.
Historically, the Catholics (who were more prevalent in New England) tended to vote Democrat, but that's no longer the case much today, so that's a non-explanation nowadays. (The distribution of Catholics has also changed in the US, to being more uniform, in tandem with the increase in Latino population. Nevertheless, the 2010 census recorded 45% of Massachusetts as Catholic.) As more general picture of religious distribution of relevance to our issue (alas in words):
There is substantial variation in religious identity between the four regions of the United States. Collectively, white evangelical Protestants are twice as large in the South (22%) and Midwest (20%) as they are in the Northeast (8%). Twelve percent of residents in the West are white evangelical Protestant. In contrast, Catholics represent a much larger share of Northeastern residents. Roughly three in ten (29%) residents of the Northeast identify as Catholic, compared to about one in five Westerners (21%), Midwesterners (19%), and Southerners (17%).
Notably, there is significant racial and ethnic variation among Catholics by region. White Catholics outnumber Hispanic Catholics by a wide margin in the Northeast (20% vs. 7%, respectively) [...]
However, despite white Catholics not being overwhelmingly Democrat nowadays, they are more split than the white Evangelicals are, e.g. in support of Trump.
So, on this dimension, New England is "double whammy" for Republicans: fewer religious people and those who are religious are more likely to be of the "neutral" religion (as far as party orientation goes).
Educational attainment (e.g. % of Bachelor's degree) seems above US average in many states in New England (at least in Massachusetts, Connecticut, Vermont, New Hampshire, Rhode Island; only Maine is [slightly] below US average). This generally correlates with Democratic party preference (and liberal ideas--the so-called "diploma divide", particularly among whites) nowadays.
The Atlantic has a interesting profile of some Republican governors in New England. In a sentence, they are lot more liberal than Republicans elsewhere on issues ranging from gun control, to climate change, to abortion support etc.
Wikipedia has bit of blurb on this topic too (supported by some citations):
Though New England is today considered a Democratic Party stronghold, much of the region was staunchly Republican before the mid-twentieth century. This changed in the late 20th century, in large part due to demographic shifts and the Republican Party's adoption of socially conservative platforms as part of their strategic shift towards the South. For example, Vermont voted Republican in every presidential election but one from 1856 through 1988, and has voted Democratic every election since. Maine and Vermont were the only two states in the nation to vote against Democrat Franklin D. Roosevelt all four times he ran for president. Republicans in New England are today considered by both liberals and conservatives to be more moderate (socially liberal) compared to Republicans in other parts of the U.S.