The first European settlers to settle in the Massachusetts Bay Colony (popularly known by the term "Pilgrims"), not counting the abortive colony established in what is now Maine in 1607 by Sir Ferdinando Gorges of the Plymouth Company, did so because they found the theological climate of their native England too intolerant of non-Anglican denominations. Many of them were Puritans, who sought religious freedom in the New World.

Merriam-Webster's Online Dictionary defines Puritans as:

Main Entry: 1 pu·ri·tan
Pronunciation: \ˈpyu̇r-ə-tən\
Function: noun
Etymology: probably from Late Latin puritas purity
Date: circa 1567

1 capitalized : a member of a 16th and 17th century Protestant group in England and New England opposing as unscriptural the ceremonial worship and the prelacy of the Church of England
2 : one who practices or preaches a more rigorous or professedly purer moral code than that which prevails

In Massachusetts Bay during the colonial period, Puritanism dominated not only theological life as the official religion of the State, but also it must be understood that Puritans controlled the political, social, and quite likely the economic spheres as well.

There were, however, dissenters to Puritanism, who would also play an important part in the development of New England. Roger Williams (1603-1683), a longtime reviler of the Anglican Church and an outspoken critic of James I of England (Not only King of England but also Ecclesiastical Head of the Anglican Church), was involved in a series of disputes between Salem and Massachusetts Bay Colonies, which eventually led, after obtaining land grants, to his departing from Massachusetts and founding a new colony at Providence which would become the foundation for the colony of Rhode Island. According to Wikipedia.org, Williams "...is often credited for originating the First Baptist Church in America, which he is known to have left soon afterwards, exclaiming, "God is too large to be housed under one roof." Thus, proto-Baptists also held some influence in the region during the colonial period.

Another dissenter of note was Anne Hutchinson (1591-1643), truly a remarkable woman in that she defied the Puritan rulers of Massachussetts by going beyond accepted doctrine to put forth her own take on Christianity, an act which would lead to her being prosecuted by the State and banished from the Colony.
According to Wikipedia:

"Soon after, Anne Hutchinson came to a new result of her philosophy. She persuaded her husband to resign from his positionAssistant Governor of the united colonies of Portsmouth and Newport, as Roger Williams put it, 'because of the opinion, which she had newly taken up, of the unlawfulness of magistry.' Anne Hutchinson had been led by her conscience and by meditation on the Scripture and logic to the conclusion of individualist anarchism."

Last, but certainly not least, one must view the native spirituality of the aboriginal inhabitants of the Region another influence. Though Christians of the time and region did not tend to convert to native spirituality, they nonetheless had to deal with it every day, as the Natives themselves had to deal with Christianity, and religious tensions between the two peoples would add to an already uneasy frontier for decades, if not centuries, to come.