The initial high profile religious conflict in America was between Calvinistic Puritans themselves (as evidenced by my two Puritan Rev. ancestors who got expelled for not following the Puritan line closely enough) and between the Puritans and Anabaptists.
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While the Puritans do have a record for intolerance for everything from Roger Williams to the Salem Witch trials — the only anabaptist communities in the colonies were mostly in Pennysylvania and mostly German, Amish, Mennonite and Heutterite. Among these I count my ancestors. Though I’m mostly calvinist now. Pennsylvania was too far away from Massachusetts in the 1600’s for there to be any interaction at all between them. I’ve never heard of English anabaptist communities in New England.
My historical read on Harvard is that that school shifted over from calvinism to unitarianism sometime in the early 1700’s. Likely largely under influence of Newton—who was an ardent unitarian. But perhaps too because the Massachusetts colonies support for Cromwell years earlier put calvinism in bad odor with the crown. (I have no proof of that.)
I'm not aware of any communities either. But no shortage of individuals with Anabaptist school of thought leanings, or at least the willingness to entertain such alternatives. Roger Williams was the most famous of these, but Crandall, Lathrop, Anne Hutchinson and others were at least open to discussion of said school of thought.