Although there was a wider variety of non-Anglican Protestants in the 13 Colonies, than Britain, I've never read anything that suggests it was portrayed as a religiously motivated war at all. After all, a lot of colonists were still Anglicans. And, while there was institutional and legal discrimination against non-Anglican Protestants in the late 18th century, it wasn't as bad as it had been in the 17th century (when many Puritans left for America).

However, one issue that did feed into the Revolution was the Catholics of Quebec. When Britain gained control over Quebec after defeating the French in the Seven Years War (or French and Indian War as it's known in America), they gave them a large amount of autonomy and religious rights (more than Catholics had in Britain, or in the 13 Colonies). Many (pre-)Americans were angry about this, partly because of anti-Catholicism, but partly because there was a large area of land that they'd hoped to get, but which Britain said the Quebecois could have. I don't remember all the details, hopefully someone else can fill in the gaps.

Non-angelicans? You mean people of non british origin?

I'm no historian, but from what I generally understand, many different religious groups were involved in the revolution and it wasn't ever a sectarian war.

Not to mention England was Anglican so that would be kind of a weird religous war to begin with.