I think that there's a fundamental fallacy in assuming that religiosity can be represented on a linear, one-dimensional graph, with Puritanism on one end, and secularism, and atheism, on the other.

Puritans emerged from a largely congregationalist sect, drawing most of their influence from Zwingli and Calvin, while the Anglican Church, from whom they dissented, also drew from Zwingli and Calvin, but not as much as from their Anglo-Catholic traditions. They also were influenced in part by Lutheranism. Rather than view Puritanism as being this "other" that emerged during the Protestant reformation, that were somehow these fringe radicals, note that they represented one side of an intraparadigmical reaction to Catholicism in the fifteenth and sixteenth centuries.