A classic example of this is the clash between John Winthrop, the Puritan governor of Massachusetts Bay Colony, and Anne Hutchinson, an early female Puritan theologian who disagreed with Winthrop over some points of Christian doctrine.
Hutchinson was brought to trial for her "errors" and banished from the colony. Winthrop writes in his journals, "Finding her to persist in maintaining those gross errors…after much time and many arguments had been spent to bring her to see her sin, but all in vain, the church with one consent cast her out."
Throughout the course of the lengthy excommunication trial, some of Hutchinson's followers were persuaded to abandon her. Winthrop writes, "Many poor souls who had been seduced by her, who by what they heard and saw that day were (through the grace of God) brought off quite from her errors, and settled again in the truth."
And what was her gross error? Basically, she advocated for "free grace" through Christ (apart from works), which is what most protestant churches today profess.
The Hutchinson trial demonstrates the fact that, for many of the early Puritans, what they sought was not religious liberty, but rather a land where their particular beliefs were dominant. Of course, given the fact that such a monolithic religion cannot exist in a world of free-thinking humans, many such clashes and schisms continued to emerge, and continue today.
One of the defining features of American Christianity has been its tendency to divide over seemingly minor points of doctrine, to the point that today there are literally hundreds of Christian denominations in the USA, each convinced that their specific set of beliefs are the "truth."