The government of Rome was held alternately by Catholic, Arian and pagan believers depending on who was able to win the personal allegiance of the armies.
The notion of a confessional state really begins with the Peace of Westphalia - and even then it is inconsistent.
You wrote:
“The government of Rome was held alternately by Catholic, Arian and pagan believers depending on who was able to win the personal allegiance of the armies.”
Okay, let’s test your theory. Please name for me all of the Arians and pagans who were Roman Emperors after Theodosius the Great made Roman Christianity the official religion of the Roman Empire.