The New England colonists—with the exception of Rhode Island—were predominantly Puritans, who led strict religious lives. The clergy was highly educated and devoted to the study and teaching of both Scripture and the natural sciences. The Puritan leadership and gentry, especially in Massachusetts and Connecticut, integrated their version of Protestantism into their political structure. Government in these colonies contained elements of theocracy, asserting that leaders and officials derived that authority from divine guidance and that civil authority should be used to enforce religious conformity. Their laws assumed that citizens who strayed away from conventional religious customs were a threat to civil order and should be punished for nonconformity.
Ministers were revered by the colonists. Although ministers were not allowed to hold political office, they made most of the important decisions. In 1636, Harvard College was founded to train Puritan ministers. It was the first college in North America.
The focus of every New England town was the meetinghouse. Meetinghouses were typically financed through taxation, and were usually the largest building in the town. They were used both for religious worship, and for conducting town business. They were simple buildings, with no statues, decorations, or stained glass. Not even a cross hung on the wall.
Despite many affinities with the established Church of England, New England churches operated quite differently from the older Anglican system in England, and from other colonies like Maryland. Massachusetts Bay had no church courts to levy fines on religious offenders, leaving that function to the civil magistrates, however, religious offenders were banished from attending church until they atoned for their offense. Essentially, the separation of Church and State at the time was that Town Meetings handled all civil matters and the Church all other matters.
The origin of the town meeting form of government still used in New England today, can be traced to the meetinghouses of the colonies.
Source: “Religion in Colonial America: Trends, Regulations and Beliefs”, Facing History and Ourselves, Brookline, MA