perfidy

In all likelihood, people associate Massachusetts with political leaders who publicly advocated, worked toward, or voted for initiatives that were left of center. John, Robert, and especially Ted Kennedy advocated or actively supported, at least publicly, civil rights legislation. Ted Kennedy, for example, incensed people in Southie, traditionally Democratic voters, when he supported public school integration. To put it simply, while the people of Southie, in general, did not support integration initiatives, their political representative did. While John and Robert Kennedy were virulently anti-Communist, Robert softened his stance in the late 1960s, and both did publicly support civil rights legislation. In other matters, Ted Kennedy has consistently voted for left of center legislation in the Senate. To mention them here would belabor the point.
Other Massachusetts politicians have similarly advanced left of center policies. Mike Dukakis, the last gasp of the left in the Democratic party, was very left of center publicly. While he was also an elitist who did not support public higher education, he was by and large left of center, and certainly more so than any other candidate to run for President on the Democratic ticket since. Machine Democrats such as Curley were also economically and politically left of center in an American New Deal sort of way, despite the racism inherent in Machine Democrat practices. Bear in mind, by the standard of the times, prior to the 1960s or even Seventies, a politician could be left of center but not a 1990s style diversity advocate. As a side note, advocates of diversity tend to be hypocritical because they don't really advocate diversity, just argue that if it's not white male it's good. But that's another post perhaps.

Beyond politicians, however, the general populace has also demonstrated left of center leanings. In 1972, Massachusetts was the only state McGovern carried. He was also very left of center, certainly by American standards. I wouldn't dismiss the labor aspect of Massachusetts. Labor is the heart and soul of the economic left. Of course, the new faux left doesn't seem to give a rat's ass about economic or political issues; it's all about wearing helmets and not saying bad things that hurt other people's feelings for them. In other words, if labor has remained important to Massachusetts, then the state is truly more left of center than people who think culture is the be-all-end-all of human existence.

In other words, I don't think that Massachusetts has been associated with Communism. I think it's been considered more liberal by the modern American definition. Of course, some John Birch types and other right of center folks did call modern American definition liberalism Communism. But they were wrong. Know why? Everyone I've mentioned above, including McGovern, was still a capitalist and an upholder of American representative democratic governmental systems. But even those MADLs of Massachusetts were from urban Massachusetts. There has been an urban/rural divide in American society pretty much from the get-go, and everywhere in the western world urban areas tend to be more progressive and rural areas conservative or reactionary. Therefore, it's mostly urban Massachusetts where MADLs can be found. So, as you correctly point out, the characterization of Massachusetts as Communist is way off the mark, but there is some justification for looking to urban Massachusetts for left of center politicians, and in some cases, populace.