In a word, irony.
 Colonial times
The first European colony in New England, Plymouth Colony, was founded by the English Dissenters, or Puritans, a group who felt that the Church of England wasn't going far enough in purging those pesky Catholic traditions from jolly old England. Feeling that the motherland was a lost cause, a group of Puritans first emigrated to the Netherlands, but like so many immigrant communities, they became worried about their next generation assimilating into the local culture. And so, a few of those Puritans, the ones we know as the Pilgrims (of Thanksgiving fame), decided to get on board the Mayflower and head to the Hudson River area to start a new life for themselves, free of both the papist C of E and the Dutch. However, the boat got lost in a storm and instead landed inside the hook tip of Cape Cod, Massachusetts. Since their charter was for them to settle at the mouth of the Hudson River, which was pretty damn far away, the Pilgrims had to put together their own government, called the Mayflower Compact.
Despite early struggles, the Plymouth Colony was successful enough that, ten years later, another group of Puritans arrived in the region. This group landed to the north of Plymouth and founded the Massachusetts Bay Colony at the mouth of the Charles River, building their settlement, Boston. Like the Pilgrims, the Boston Puritans came to the New World for religious freedom. And in that, we get New England's first irony: the Massachusetts Bay Colony promptly set up a theocracy that denied that very same freedom to anybody who dissented from its religious authorities. The guy running the colony, John Winthrop, wanted Boston to be a "city on a hill" to symbolize the virtue of Puritanism, and to do this, he set up strict standards of morality and persecuted non-Puritans, especially Quakers. Eventually, a number of people in Massachusetts grew so upset with their colony's theocratic government that, in 1636, a group led by Roger Williams left and set up the Colony of Rhode Island and Providence Plantations, where religious freedom would be assured. Two years later, Thomas Hooker led the foundation of the Connecticut Colony for the same reason. While King Charles II would eventually step in in the year 1661 to prevent the Puritans' worst abuses, Massachusetts remained a very, well, puritanical place, as evidenced by the fact that the only organized witch hunt in the American colonies was carried out there in 1692.
In 1686, the short-lived Dominion of New England was set up, merging Massachusetts, Plymouth, New Hampshire, Rhode Island and Connecticut (and, later, New York and New Jersey) into one colony. Not only was it too big for one governor to manage, but said governor, Sir Edmund Andros, was, by all accounts, a major-league prick who pissed off just about everybody in the colonies. The Dominion of New England was dissolved in 1689, just three years after it was created.
New England was the birthplace of the American Revolution, between the Boston Massacre, the Boston Tea Party and the Battles of Lexington and Concord. After the revolution, we get into Irony #2 — during the War of 1812, New England, despite having been the first place to rise up against the British the last time, was the region where pro-British sentiment ran the highest. To the point that, at the Hartford Convention, they seriously discussed seceding from the U.S. over the fact that they were at war with Britain. This time, however, the situation made a fair bit of sense — New England's economy rested upon trade, particularly with Britain, which was cut off for the duration of the war.
New England was the first part of the country to industrialize, and with it, it was also the first part of the country to unionize. You can bet that this has colored its politics ever since.
Starting in the mid-19th century, Irish Catholics started to mix in with the English Protestants. Irony #3 — the fact that a region that had been founded as a refuge from Catholicism was now turning into the American Catholic heartland — was not lost on the original inhabitants, who reacted as you might expect, claiming that the Pope was throwing waves of Catholic immigration at America in order to subvert it and make it bow to the Holy Mother Church in Rome. That, on top of the usual racism and "they're taking our jobs!" rhetoric that is usually thrown around by nativists. Even so, New England's reputation for puritanical moral guardianship changed little, with the Catholics making for just as efficient culture police as the Puritans. All the way into the 1950s, the Watch and Ward Society, composed of both Catholics and Protestants, made "banned in Boston" a phrase that people would attach to their books, plays and movies in order to drum up publicity.
This puritanism is, however, contrasted by social liberalism. New England is a Democratic stronghold, and even in those areas that swing Republican (New Hampshire, for instance), the conservatism is more libertarian than religious right. This is New England's Irony #4 — that a region that, for all of its history, had been so uptight could also be so remarkably progressive on so many issues. New England, more so than the rest of the North, was a hotbed of abolitionist and feminist sentiment, and more recently, the first four U.S. states to legalize same-sex marriage — Massachusetts, Vermont, Connecticut and New Hampshire — were New England states. It has also provided America with Bernie Sanders, the only open socialist in the Senate. At the same time, well, "banned in Boston" sums it up, and if you think that it's any different now, keep in mind that, in the state of Massachusetts, tattoo parlors were outlawed until the first decade of the 21st century.
And on top of that, there's Irony #5 — the direct descendants of the old Puritan congregational churches, the United Church of Christ and the Unitarian Universalist Church, are the most liberal Christian denominations in America, and possibly the world, throwing their support behind gay rights and other socially progressive causes.
From John Winthrop to Barney Frank, indeed...