There are a number of ways of answering this question and it's a little difficult to answer definitively but I'd offer that education is one of the factors that has contributed to Massachusetts' evolution.

One of the foundational sentiments in the Massachusetts Bay Colony was the need for basic literacy as a way to fend off Satan. The first recognized compulsory education law in the colonies was passed in Massachusetts and was known as Old Deluder Satan Law. It reflected the community's belief that literacy and education were a net good. Granted, the focus was mostly on their sons' souls and their daughter's future role as wife and mother. This sentiment would eventually evolve into the notion societies are stronger when the government provides free (i.e. no tuition) education to future voters, workers, mothers, and citizens. Generally speaking, communities that value(d) universal education tend to be more liberal.

Massachusetts is also the home of the oldest high school in the states (Boston Latin School) and the oldest colonial college (New College, later known as Harvard.) Although they would eventually move to other regions of the Northeast, Quakers originally settled in the Massachusetts area and brought with them a commitment to universal education for daughters and sons as well as an early American sense of social justice (anti-slavery, anti-war.) It wasn't unusual for a Quaker school to accept free Black children or escaped enslaved families and support their literacy efforts. Likewise, Harvard was home to the Indian College, which - to be clear, was focused on providing Indigenous men and boys a Christian, European education and not an education of their own design and choosing - allowed interactions between the European-American boys and Indigenous youth. In a sense, these early interactions set the ground for a tentative approach to integration and desegregation.

The "common" schools movement had its origin in Massachusetts and would eventually lead to universal, secular, compulsory education across the country. To be sure, it was steeped in institutional sexism and white supremacy but at the core, the idea of education as a public good is deeply progressive.

The first effort to desegregate schools came more than a century after the Old Deluder Satan Law. Prince Hall, a free African man living in Boston tried to get legislation passed in 1787 that would provide for funding for Black schools on par with white schools. Although he was unsuccessful and just one of the many attempts, he tested the system around the concept of equality and equity, i.e. liberalism. The 1850 case, Roberts v. City of Boston, is recognized as the first attempts to desegregate public schools and although it would be used in Plessy v. Ferguson to hold up the idea of "separate but equal", the arguments on behalf of Sarah Roberts would eventually be used in Brown v. Board of Education.

In effect, parents of marginalized children have been pushing for access to universal quality education for their children for centuries and many of those fights happened in Massachusetts. Their efforts meant that the state's governing structures had to learn to respond (and they often responded in a way that uphold a segregated system) but the language and precedents were in place for other groups to fight for equity and equality.