Final answer:
Roger Williams and Anne Hutchinson were the two most famous individuals banished from the Massachusetts Bay Colony for dissenting against the Puritan church and state acts.
Step-by-step explanation:
The two most famous individuals who were punished for not complying with the church and state acts in the Massachusetts Bay Colony were Roger Williams and Anne Hutchinson. Both of them clashed with the Puritan authorities due to their dissenting religious views.
Roger Williams, a Puritan minister, questioned the Puritans' taking of Native land and advocated for a complete separation from the Church of England. He was found guilty of spreading 'dangerous ideas' and was banished, later founding Rhode Island, a refuge for those seeking religious freedom. Anne Hutchinson was also banished for her unorthodox beliefs and practices which challenged the Puritan orthodoxy.