Well, although a number of Episcopalians joined the rebellion, it tended to be people who had a problem with the Established Church of England.
In the mid seventeenth century, it was the Presbyterians who led the way in the Civil War and Puritan Revolution. But in the late seventeenth and early eighteenth century, some of the chief opponents of the Hanoverian rule were Scottish and English Catholics, who fought several times to try to restore the House of Stuart to the throne. See several of Walter Scott’s novels for some good accounts.
And in the American Revolution, Catholics played an important role—notably the Maryland Catholics such as Charles Carroll of Carrollton—who put up a ton of money to support the rebellion and was one of the signers of the Declaration of Independence.
So, perhaps oddly from the perspective of many of the Catholic-baiters on this thread, it was a coalition of Puritans and Catholics, among others, who defeated the British.
The Puritans like the Presbyterians were Calvinists. Most of the colonists outside of Episcopalians were Calvinists. and the Episcopalians at the time were much more reformed than they are today.
Besides the Presbyterians and Puritans, the Dutch, German, Swedish, Swiss Reformed churches scattered about the colonies were all Calvinists. As were the small number of French Huguenots.
Why Calvinists? The Calvinists were the big losers of the wars of the 17th century all over Europe.