The (crass and recent) counterpart to Catholic integralism is Evangelical dominionism, and they are both antithetical to the worthy aims of a secular democratic republic where we must privilege no faith so that people of all faiths and none stand on equal ground as citizens with the same rights and freedoms. This may not be the vision of the Kingdom of God on earth, but it is certainly preferable to Spain under Ferdinand and Isabella, Geneva under Calvin, New England under the Puritans, or—God help us—America under some crackpot Dispensationalist trying to bring about the Rapture.
I'll take a bright line of division between church and state any day, relish the spectacle of the wheat and the tares sown together in the field, and give thanks to God that the state as constituted here cannot legally function as the temporal arm of any organized or badly disorganized religion.
In the meantime, ping me when the anti-abortin voters, either Catholic or Protestant, are equally interested in abolishing the death penalty and removing the weapons of war from their place of honor in American life and culture. Come to think of it, ping me when either of the two political parties takes that stand.