Not true. Most of Britian's immigrants who consisted of the Mayflower's population were indeed Christians. If you look throughout history, while you can say the God is not specified, it is indeed the Christian God, because of the teachings. If you compare their teachings to Christian beliefs, it was completely and totally centered around Christianity. For example, Witches were burned at the stake. Why? Because they were the enemies of Christianity, since they are closely related to Satanists. While this is extreme, this is one of the many things just like adultry which was severely looked down upon by Christian influence