The two most influential groups around Boston and in Massachusetts generally are the old white Protestant families, commonly called Boston Brahmins, and the Irish, formerly laborers and maids of the Brahmins.
The Brahmins controlled everything until the Irish multiplied and got themselves into office. They were typically represented by the great Mayor Curley, James Michael Curley, one of the first of the corrupt Irish machine politicians in Boston.
I think the Irish got tired of being discriminated against and figured it was better to stick together and support the machine. A little corruption was OK as long as it was the Irish doing it and taking care of their friends. Other ethnics fell into line because they lacked the numbers to do it themselves and still resented the Brahmins.
Some of that attitude probably still lingers. Plus now many of the white Protestants are liberals, willing to vote Democrat no matter what. These two groups give Kennedy a solid base of support no matter what he does.