To my understanding, there existed a time in early American history, before the Declaration of Independence was signed, when several states had established state churches, reflecting traditions inherited from England by the initial settlers.
Well, kinda.
These established churches weren't so much a reflection of English traditions, as they were a rejection of English religious tolerance. The English established church was far less dominant in England than the colonial established churches were in their respective colonies.
In particular, the puritans fled England in order to find a place where they would be allowed to impose puritanism on everyone, something that they were unable to do in England.
The North American colonies prior to the American Revolutionary War were in many cases considerably less free, and considerably less tolerant, than England, on questions of religious observance.
There was also less personal liberty. Slavery was obviously a central part of colonial life, in a way that it hadn't been in England since the Romans left; but even for "free" settlers, the individual colonies typically had much stricter rules about how to behave than were found in England at the time, and less room for those who would not comply to get away with their attempts to avoid or subvert the rules.
Like sea captains, the leaders of the various colonies typically had almost absolute authority to do as they wished, other than in matters of broad policy. They were hypothetically answerable to the government in London, but as communications with that authority were slow, infrequent, and completely under the control of the colonial governors (or more often, lieutenant governors, as the governors rarely set foot in the colonies they were nominally in charge of), they were
de facto absolute dictators, answerable to no one, at least in regards to the daily lives of their citizens. As long as the tobacco and cotton and revenues and taxes kept flowing.
It would be tempting to think that the overthrowing of these dictatorial (lieutenant) governors was a central factor in the Revolution itself; But the sad fact is that these are mostly the same people who were the leaders on both sides when war eventually broke out.
Freedom (religious and otherwise) was a side effect of the American Revolution; The autocratic leaders of the colonies were forced into it as a compromise to prevent the fracturing of their stand against English authority. They had to hang together, or they would all be hanged separately; And that meant they had to drop many of their existing strictures, such as established religions, lest the conflicts between them became insurmountable.
Freedom was (and remains) a direct consequence of diversity. When everyone agrees, they can more effectively be represented by a single dictator than by a committee; But when there is diversity of opinions, the factions can only be represented by compromises amongst a diverse parliament of rulers, and in the areas in which disagreements are intense, the only way to avoid conflict is by giving all sides the liberty to do as they desire, without fear of being imposed upon by the others.