I know that Massachusetts was home to socially progressive movements (abolitionism, women's rights, prohibition) in the 1800s. What changed between the Puritanical attitude of social conservatism of the 1600s and the liberalism of the 1800s?
Boston was (and is) a major seaport on the eastern seaboard. If you look throughout history, cities that feature a lot of trade don't only trade in goods, but also culture and ideas. This is, arguably, the reason that any major metropolis tends to be more liberal than their smaller counterparts -- a diverse ethnic and cultural spectrum within the population contributes to empathy and an exchange of values/ideas that simply can't happen with a less diverse population. There's also the fact that major metropolitan areas tend to spawn prestigious places of learning in the area. I know this isn't all of Massachusetts, but over 70% of the state's population lives in Greater Boston (based on the most recent census figures). Boston's strategic location as a major trade and industrial center is what turned it into the 10th largest metro-area in the US, and metropolises tend to be liberal.
A great example of this is Atlanta. It's dead in the middle of one of the more staunchly conservative states in the union yet, because of its relatively large, diverse population it tends to lean significantly farther left than the rest of Georgia. Another good example is my state: Virginia. The rural areas are extremely conservative, but Richmond, the beach area, and northern Virginia tend to lean more liberally. They are like that because of the strong military/government presence in the area that attract employees from all over the world, as well as large representation of African-Americans (Richmond is majority African-American as of the last census). EDIT: It's also worth mentioning that, as the metropolitan areas of the beach, DC, and Richmond begin to overlap and expand, even more rural areas are becoming more liberal, as they transition rapidly from rural, agricultural counties and towns to so-called "bedroom communities". Virginia is rapidly becoming a battleground state for federal politics for many of the same reasons Florida has been one for the past 50 to 60 years: a large transplant population, and rapidly-expanding urbanization. Before Disneyworld, Orlando (and most of Central Florida) was nothing more than swamps and orange-groves.
I know this is getting dangerously close to current politics, but I just wanted to illustrate how major metropolitan areas and diversity can drastically change the political landscape of otherwise conservative areas.
Is prohibition considered to be a socially progressive movement? (I'm assuming you're referring to the prohibition of alcohol that culminated in the 18th amendment and the Volstead Act in the early 20th Century).
I would have associated prohibition more with the previous puritanism rather than more liberal attitudes.
Well not directly related, a lot of the cities that sprung up during the early-mid 1800 in the area were filled with immigrants looking for work, and the area became a general melting pot of cultures. This had a lot to do with the start of the industrial revolution and rise of quite a few mill cities, especially in the Merrimack Valley (Lowell and Lawrence are the most famous). These cities were hotspots of a lot of these progressive movements, and new technological advances as people came and left the mill industry.
An interesting (although Historical Ficiton) novel to read on the subject would be Call The Darkness Light, which primarily takes place in Lowell during this time.
Ok, this probably isn't worthy of a top-tier comment, but perhaps you should look up "Banned in Boston" and the Comstock laws. The puritan authoritarian streak still exists in a different form.