It's been tried before. Usually ends badly, at least by the standards of the modern day. Research Auto Da Fes and get back to us.
Not just Catholic Theocracy that's a bad idea either. ANY totalitarian state seems to go the same way.
yeah, Auto Da Fes of the Spanish Inquisition were an abuse of Religion and State power.
abuses happen with any system.
America has had Separation of Church and State (to one degree or another) since 1776, and we have also had
slavery
genocidal actions against the Indians
monopolies that harm worker and consumer rights
Japanese being thrown in internment camps.
every system has its good moments and bad moments
I am not calling for the Spanish Inquisition to come back
here is what I think a modern "Catholic Country" could look like, under a Constitutional Monarch or a Republic of some sort
the government to be able to give money to Catholic Charities without tying their hands about not preaching or stuff like that.
Catholic charities, schools, and other public programs run by the Church would be favored over those of other religions. So if the Baptists wanted a school, they could have it, but it would not get any tax payer support while public Schools would be basically Catholic Schools.
things that are clearly against the faith would be illegal, such as abortion and inappropriate contentography, prostitution.
It is VERY likely that there would be black market for these things, just as there is for prostitution now. How hard the government would want to go to enforce such laws is a matter of prudence, like other religions, it makes sense to tolerate a certain level of vice, the main thing is that the law is not used to protect or support such actions
Sunday rest for workers
a few other things, maybe a slightly stricter public decency laws.