It was "Protestant" ministers that were were supported. Even Unitarians were considered "Protestant."
Read for yourself what the Massachusetts Constitution said:
...the people of this Commonwealth have a right to invest their legislature with power to authorize and require, and the legislature shall, from time to time, authorize and require, the several towns, parishes, precincts, and other bodies-politic, or religious societies, to make suitable provision, at their own expense, for the institution of the public worship of GOD, and for the support and maintenance of public protestant teachers of piety, religion and morality, in all cases where such provision shall not be made voluntarily. And the people of this Commonwealth have also a right to, and do, invest their legislature with authority to enjoin upon all the subjects an attendance upon the instructions of the public teachers aforesaid, at stated times and seasons, if there be any on whose instructions they can conscientiously and conveniently attend. Provided notwithstanding, that the several towns, parishes, precincts, and other bodies-politic, or religious societies, shall, at all times, have the exclusive right of electing their public teachers, and of contracting with them for their support and maintenance. And all monies paid by the subject to the support of public worship, and of the public teachers aforesaid, shall, if he require it, be uniformly applied to the support of the public teacher or teachers of his own religious sect or denomination, provided there be any on whose instructions he attends: otherwise it may be paid towards the support of the teacher or teachers of the parish or precinct in which the said monies are raised.
Here is some information on the struggle to establish a separation of church and state in Massachusetts. The source is the great Sanford Cobb's "The Rise of Religious Liberty in America: A History."
The struggle in Massachusetts was more protracted. There was the same political adoption of the Church question as in Connecticut, perhaps with a shade less of bitterness, while to this was added another element which threatened the very existence of the old Puritan Church.1 The strife began promptly on the adoption of the constitution of 1780, which some of the dissenters construed as exempting them from filing certificates of dissent and from payment of tithes. To test the claim a Mr. Balkom of Attleboro, in 1781, refused to pay and, the tax having been collected by levy, brought suit for its recovery. The case went against him in the justiceâs court, but on appeal to the county court the sentence was reversed. This should have settled the question for the State, but it did not, and the old custom still generally obtained.
Some years afterward, a Mr. Murray, a Universalist minister, brought suit for recovery of tithes paid by his parishioners. In defence the Stateâs attorney argued that âa minister, who denied the eternal punishment of the wicked, was not a teacher of piety, religion, and morality,â within the meaning of the constitution! But the court gave decision for Murray, and in 1799 the legislature passed an act allowing such suits for recovery, from which act a later decision of the supreme court took much of its life by deciding that ministers of unincorporated societies were not public teachers, and therefore could not claim the privileges of the law.
Meanwhile the Unitarian defection was gathering force and under the law had an immense advantage, so soon as it could persuade a majority of citizens to its views. The law made the Church a town institution, and gave the choice of minister to the town meeting. It was thus easily possible for the town meeting to override the orthodox portion of the community. This danger made itself evident in the great Dedham case, the issue of which was so momentous for the Church of Massachusetts.
The majority of the Dedham Church were orthodox, while the majority of the town were of Unitarian proclivities. In 1818 the minister of the Church resigned, and the town chose a Unitarian as his successor. The Church refused to assent to this choice, and the case was carried to the supreme court, which decided that the constitution âgives to towns, not to Churches, the right to elect the minister in the last resort.â This decision gave the Church perquisites and property to the Unitarians, and the Orthodox were forced to make a new Church for themselves on the voluntary system. A like result followed in very many places, and the old Puritan Church found itself turned out of house and home by the very powers it had contrived to give it lasting security. This was the death-blow to the long-moribund theocracy. The constitutional convention of 1820, following the erection of the State of Maine, attempted to meet the religious question, but through the opposition of the conservative element succeeded only in the abolition of religious tests for office. In 1833 the Church was finally disestablished. Tithes were abolished, the voluntary system made universal in the state, and the towns discharged from all concern and power for Church affairs.