Pilgrims Going to Church, oil on canvas, 1867, by George Henry Boughton
This is a common misconception, mixing the two quite different approaches to the Protestant religion.
The Pilgrims were actually called Separatists. Separatists believed that the only way to live according to Biblical precepts was to leave the Church of England to worship in their own way.
Separatists rejected idolatry, trappings, and all sacraments (except for baptism), along with all holidays, including Christmas. Thus confession, penance, confirmation, ordination, marriage, and last rites did not exist in their religion. Separatists viewed them as inventions of the Roman Church, had no scriptural basis, and were therefore superstitions. They had no building designated as a church. They could meet anywhere and the place would simply be called a meeting house.
Separatists attempted to keep their religion apart from their government, as written in the Mayflower Compact. You could be a citizen in the Plimoth Colony but not be a Separatist (you did have to pay taxes!) This is why people who practiced other forms of religion, such as Quakers, were generally tolerated.
Puritans wanted to reform the Church of England from within and kept many of the practices, including the sacraments. Idolatry – paintings, statues, etc. – could be seen in the churches they built.
The Puritans’ religion and their government (of the Massachusetts Bay Colony) were intertwined. Other forms of religion were NOT tolerated, and their practitioners were persecuted.
Both Puritans and Separatists shared a form of worship and self-organization called the congregational way: no prayer book other than the Bible, no formal creeds or belief statements, and the head of the church was Jesus Christ.
And for both Puritans and Separatists, their members (only men) made decisions regarding their religion, such as the selection of their leaders, democratically.
Thus in The Last Pilgrim, there are no formal marriage ceremonies, just gatherings to celebrate after these unions were noted in the colony’s records. There is some interesting tidbits about baptism: one of the most heated discussions at that time was whether baptism should be done by immersing the baby in water or just sprinkling water on the head!
I couldn’t get into this distinction in-depth in the book, so this was part of my background rsearch.