Interesting statement. I thought that 11 out of the original 13 colonies had Calvinist state religions and drove Catholics, Baptists and Quakers out (or killed them).
Only Massachusetts, Connecticut, and maybe New Hampshire(I’m too lazy to look it up) had Calvinist state religions. That is only 3. What you describe would be the 17th Century, the founders lived in the 18th Century as men of the Enlightenment.
The colonies had issues with established religions, yes, just as European states did. The colonies may have been controlled by England and many had established the Church Of England, but others had not. Our colonists had varying origins and various religious beliefs. The Roman Catholic Church was undeniably a State Church before there ever was a Protestant State Church, however, and so it is the original State Church.
Only the New England colonies did that sort of thing. As far as I know the only people actually executed for religious dissent were Quakers. Oliver Cromwell put a halt to local executions in New England in the 1650's after the execution of Mary Dyer (executed against his orders) and there were no executions of religious dissenters after that. During the Salem witch trials they were executing fellow Calvinists.
All 13 had state religions, though the degree to which they tolerated those who were not part of the religion varied. New England tended towards Calvinism. Maryland south tended towards Anglicanism.