“New Englanders, like John Adams, felt that State should care about religion and religious education, requiring towns in MA to pay salaries to preachers.”
Adams wrote Massachusetts’s Constitution of 1780. But there were test oaths mandated that effectively limited some public offices to Protestant Christians. (The amount of anti-Catholic bigotry in the US back then is shocking to modern sensibilities today and Adams was one of he bigots.)
Furthermore the religious education you mentioned was Puritan. Had their been any Jews in Massachusetts back then, we would have had to pay taxes to support the Puritan religious schools, as were Christian minorities.
Adams would die in 1826 and Massachusetts would finally distablish its Puritan Church (by then, largely Unitarian in the eastern part of the state) in 1833. The first Jewish religious congregation would not be started until 1842. Like every other Ashkenazi congreatation in existence in the US at that time that has survived, it is not orthodox.