It would probably be a world very like the one described in The Handmaid’s Tale, by Margaret Atwood. As the author says here,
Like any theocracy, this one would select a few passages from the Bible to justify its actions, and it would lean heavily towards the Old Testament, not towards the New.
Further, in order to reply more fully to @rockfan, like all settled societies, there would be stratification by social class, however determined. To enforce its will, the State would have to be a dictatorship. Through the government agencies, it would control the country’s physical and other resources. By the way, has anyone looked at Leviticus, especially the chapters that deal with the duties and entitlements of the Levites? By the time of the Common Era, it was obvious that the Levites had become corrupted. They controlled a large part of the nation’s resources and no longer answered to the people.
My answer assumes that we are talking about a modern country endeavouring to become an Old Testament state. Such a place would be undemocratic, violent and cruel. It could not be otherwise.