During the time when there were New England colonies, such as Massachusetts, Connecticut, and Rhode Island in America, what different religions existed? And did those different groups get along?
During the Colonial Era in what is now the United States, there were a number of different Christian sects. There were also some Jews. However, the country was very much dominated by Christian religious groups. There were, perhaps, not as many different sects as there are now, but there were a fair number. Among the religious groups were Roman Catholics, Presbyterians, Anglicans, Congregationalists/Puritans, Lutherans, Methodists, Quakers, and Baptists. There were also, at least after the Great Awakening, some splits between different factions within the sects.
As to the question of how these groups got along, it is hard to answer in any way that covers all of these groups. For the most part, the groups got a long decently. There were not any religious wars or serious violence between groups. However, particularly in New England, there were important conflicts. This was most prevalent in New England because there were many Puritans there. The Puritans believed that they needed to create a theocratic society that would be run according to the will of God. This made them rather intolerant of other groups. In those colonies, then, there were more conflicts between various religions than in other colonies.