That's unfair. Most religiously active Americans at the time of the Revolutionary War belonged to denominations which had an established antipathy towards established religion- Presbyterians, Congregationalists, Methodists, and so on. Scotland and the United Provinces, two very important (if in the latter case more indirect) influences on American religious life, were dominated by Calvinist churches, but no movement was ever made to establish those churches, before or after the Revolution.
The trick is that they were concerned about government intervention in religion, rather than religious intervention in government. That was understandable, given: England, but turned out to be unfortunate in the long run, given: America.