Why were Anne Hutchinson and Roger Williams banished?

They decided to arrest her for heresy. In her trial she argued intelligently with John Winthrop, but the court found her guilty and banished her from Massachusetts Bay in 1637. The ideas of religious freedom and fair dealings with the Native Americans resulted in Roger Williams' exile from the Massachusetts colony.

Explanation: there ya go.

They decided to arrest her for heresy. In her trial she argued intelligently with John Winthrop, but the court found her guilty and banished her from Massachusetts Bay in 1637. The ideas of religious freedom and fair dealings with the Native Americans resulted in Roger Williams' exile from the Massachusetts colony. Religious dissident Roger Williams is banished from the Massachusetts Bay Colony by the General Court of Massachusetts. Williams had spoken out against the right of civil authorities to punish religious dissension and to confiscate Indian land.

Explanation:

But within three years, Anne Hutchinson would stand before a Massachusetts court, charged with heresy and sedition. In 1638 she would be excommunicated from the church and banished from the colony for holding and teaching unorthodox religious views. Anne inherited her father's intellect and strong religious beliefs. They argued against the members of the Massachusetts clergy claiming that they had no right to spiritual office. Hutchinson and Williams were a serious threat to the Massachusetts Bay as they would go around claiming that the clergy was not amongst the elect.