Oh, my no, it's far more complicated than that. Catholics from the English civil wars settling in Virginia. Other remnants of the English aristocracy who were not Catholic, especially Montrose's followers, the same. Protestants butchering other Protestants in England, Germany, the Netherlands. Calvinists versus Anglicans. And everybody versus the Jews. All of this bled over into the New World and at some point the people there became sick of it. Certainly they were mostly Protestant but even more, they were sick of killing other people over it.
What happened in Europe from about 1618 on was that people went from killing one another over religion to killing one another over nationality and politics. I'm told it was an improvement but then I'm told a lot of strange things. ;-)