@aroosi
Well, as to the utopic or nightmarish
qualities of the place, that would really depend. Even religious communities have their problems, which is why utopias tend to be fictional
I think the main difference would be that the government would be supportive of Catholic activities and principles, one of which, remember, is the civil right of people not to be forced into Catholicism.
But we might have more Catholic holidays
as they did in the Middle Ages, for example, and prayers broadcast on the radio, like the Angelus at 6 am, noon, and 6 pm.
People would be more educated in Catholic principles, and use them as a basis for making decisions, but to be honest, religious influence on government is a spectrum. I lean towards more than we have now in the US, but less than the type of control that existed during the establismentarian systems in the [US] colonial times, when, for example, people were required by law to go to church on Sundays or pay a fine.
(I do not in any mean to imply that the US ought to move in that direction, which I would see as totally impractical, only t ok describe a position on the spectrum.)