How were the pilgrims persecuted in Europe?

The Pilgrims were not Puritans (who wanted to "purify" the Church of England from within) but Separatists, who wanted to get out of it entirely. This was not legal in those days--almost all European countries required people to follow the same religion as their king. Anyone who didn't was subject to discrimination or persecution, depending on how uptight the local ruler was.

In England, Catholics, Jews, Separatists, Baptists, Quakers, and admitted atheists were all equally in troubleOne of the few places that offered religious freedom was the Netherlands, so the Pilgrims moved there. However, they were staunchly English, and they didn't like it that their children began assimilating into Dutch society. Few people know that the Pilgrims actually set out not from England but from the city of Leiden in the Netherlands.

Although both the Pilgrims and the Puritans were stern, NOBODY ever burned witches in the U.S. There was only one set of witchcraft prosecutions in North America, the infamous Salem trials of 1692, and the condemned were hanged, not burned. The Pilgrims and Puritans were both Calvinists, but over the years, they evolved into two of the most liberal denominations in America, the United Church of Christ (UCC) and the Unitarians.