The Articles of Religion were written just so to establish a definite and firm disagreement with their theology.
The Puritans however are not Anabaptists but Calvinists. The same ones that made a martyr of the good St. Charles Stuart I. They were not very nice people, even to their fellow and more moderate Calvinists, banning Christmas and secular sport, not to mention driving Anglicanism into the underground. And don't get me started on how they celebrated their "freedom" in the New World.