You are missing the point:
A “state religion” is about as significant as a “state bird” after the constitution has been ammended to guarantee freedom of religion. When the “state religion status” was written into the consitution, it meant something very different. Now, it typically signifies that an overwhelming percentage of the population practices one religion. Compare that to what goes on in places like Iran. Yes, the US was somewhat unique in stating specifically that we would never have a state religion. Regargless, there are no countries other than the Holy See and perhaps Monaco (I didn’t bother to check because its a monarchy and its irrelevant) where Catholicism is still the official state religion in practice.
You seem to believe a “state religion” or “official religion” by definition means persecution or illegality of all other religions.
I disagree. It means there is an established religion, that a particular religion is supported and recognized by the state, but does not necessarily mean other religions are persecuted.
In any case, there are a great many countries where practices that Americans would view as a violation of the “separation of church and state” are commonplace.