The reason he left the Harvard presidency was that he refused to have his children baptized after becoming convinced of Baptist views, which at that point were being tolerated under Oliver Cromwell in England but were still unacceptable in Massachusetts. Dunster left Massachusetts and accepted a pastorate in one of the churches of the then-separate Plymouth Colony.
Being forced to leave Boston and move to a more friendly colony is not exactly what I'd call serious persecution, especially compared to what was happening in Europe at the same time.
Great stuff. Thanks for the education.