It has to be centred around the Reformation. Say Henry VIII cuts ties to the Catholic Church, paving the way for Protestantism as per OTL. However Henry becomes more and more power-mad, not just as a King but a self-proclaimed Pope in his own right. The Revolution is bloody, and basically all remnants of the hated church are destroyed in a civil war to rival the OTL war of the roses or the english civil war. Out of the ashes rises an extreme form of Protestantism which rejects not only crosses and 'idolatry' but the churches themselves, any organised hierarchy and is deeply suspicious of preachers, even much of the Bible is very heavily questioned and criticised. The ruling classes who led the religious crusades and witchhunts are mostly dead, leaving a sense among the common people of all religions having caused them nothing but misery. Added t this is a very real fear that if they show any outward signs of following any 'side' they will be targetted by the other, especially if they are suspected to be Catholic.
As the enlightenment continues, scientists and freethinkers fleeing Catholic Europe add to an overall sense of religious freedom, the resultant surge in technological progress and industrial revolution is seen as a sign of gods 'approval' rather than the work of the devil.