Religion was not a major cause of the American Revolution. However, it may have influenced the way that people viewed the colonies and the British. The Great Awakenings of the 18th century did not cause the American Revolution, but they may have created a way for communities to be more united as a whole. We know that colonists came to the new world seeking freedom of religion, but the Revolutionary War took place in a different era than when the first colonists arrived. The Continental Congress actually wanted to work things out with King George in the Olive Branch Petition. The King, did not wish to address any of their grievances.
From a Biblical perspective, one might suggest that the British were like the Egyptians and the colonists were in bondage. However, I am not aware of any historical evidence of this viewpoint or any that are related to this.