Exactly. I was questioned several times about that post, and in the end wrote pretty much what you did. The Constitution is entirely neutral about what the states decide to do about religion. Several of them, notably Massachusetts, had what amounted to rule by church elders. Massacusetts had more blue laws than any other state, and they were still around until the late 1950s, when they began repealing them.
If you didn't like it, you could move to Connecticut or Rhode Island like Anne Hutchinson.
And the thought that you couldn't teach religion, the Bible, and morality in the schools would have been inconceivable until some time around the middle of the twentieth century. One of the major purposes of education was to teach kids the moral rules. Now all you are allowed to tell them is, "Be nice. Don't be judgmental. Tolerate everything."
One of the major purposes of a true education is moral instruction. Anything less is child abuse.