Absolutely! In the previous 100 years the pendulum swung between “burn the priests!” And “quarter the Protestants” so when the of Charles the 1st came around it seemed like there was to be a reprise of such things, and not necessarily with any clear winner until the end. Tracing some histories you will find a few distinct groups; those who had lost their fortunes, those who hoped to preserve them by establishing new opportunities in the New World hoping things would blow over by then and those who were genuinely escaping religious persecution, not because they were tolerant but because they were so intolerant, so fringe. And many more…quakers to Philadelphia and NY, Catholics in Maryland colony

Also, America wasn’t America, so to speak. One went to Salem or Plymouth to live the pious life, where Boston, the entry to massachusetts colony was renown for its collection of dregs who have fallen out of favor with god. No doubt, many were opportunists looking for a new start. Rhode Island was home to a more diverse group, as Roger Williams may have been a very religious man he did not disdain those who harbored different beliefs. Depending on your motivation, you took a particular ship to a specific destination. It was no small task to swap Plymouth for Virginia, as there was more transatlantic travel than there was inter coastal.

But more to you point, yes, leaving an England once again cleaving itself in two, was a cause, though not THE cause. By the 1650s there was a lot of opportunity, especially in the Mohawk valley of NY and the areas radiating out from Philadelphia, Baltimore and the Chesapeake. A little servitude or a payment to cross, become a freeman and get some land. Unless you were a slave…