The States were not perfectly free, at the time of the founding, to have established religions. The people in ten of the States would have found any fool what suggested a legal establishment of religion and tossed his miserable butt into the American Religious Liberty Hall of Shame alongside that Patrick Henry.
The people of seven States had already stripped their governments, both “on paper” and in real life, of authority to establish religion. Georgia, Maryland and North Carolina had some meaningless “only on paper” religious authority. The authority did not derive from the consent of the people (it came from the old colonial charters) and was therefore never exercised by any of the three States.
In summary, in 1789, ten of the thirteen States had placed the demonic notion of government religion on a fast track back to little horn. Ten States claimed no religious authority they were interested in preserving and would not have been motivated, in the area of religion, by the desire to preserve a State's Right.
Regardless of whether or not any state had an established religion...all would have been free under the First Amendment to the US Constitution to do so. Whether or not state constitutions or state laws provided otherwise is something else. In New England, Congregational Churches received public support into the 19th century in, at least, NH, Connecticut and Massachusetts.