If that's the case, what might a more healthy relationship with the state look like?
One answer comes from "A Letter to Diognetus," a piece of early Christian apologetics from the second century. In the letter, the author describes how Christians relate to the nation states in which they dwell:
Christians are indistinguishable from other men either by nationality, language or customs. They do not inhabit separate cities of their own, or speak a strange dialect, or follow some outlandish way of life. Their teaching is not based upon reveries inspired by the curiosity of men. Unlike some other people, they champion no purely human doctrine. With regard to dress, food and manner of life in general, they follow the customs of whatever city they happen to be living in, whether it is Greek or foreign.
And yet there is something extraordinary about their lives. They live in their own countries as though they were only passing through. They play their full role as citizens, but labor under all the disabilities of aliens. Any country can be their homeland, but for them their homeland, wherever it may be, is a foreign country.