Yet it pays to remember that Jesus (and Paul, Peter, James, John) say little or nothing about this. There is a great deal said about our responsibility toward the individuals we encounter and the church community we live in, but other than rather disassociated good citizenship and not being a bother, they don't say much about amking over society in a godly direction.
The OT tells the Jews a lot about making over their whole society, but their whole society was a religious community. I don't see strong NT indications that this automatically carries over to citizenship in Hillsborough County or the Province of Saskatchewan. What if it is entirely unimportant, so that American Christians of both the right and left - both the "If my people" and "Least of my brethren" crowds - are simply wrong, reading in their political beliefs.
If the world truly is going to hell in a handbasket, so that default culture was so selfish and hedonistic as to be not worth retaining, would it be so terrible if Christians simply said "Our people chose not to participate," and let the world go as it would without us? One might read the Revelation to John as being a record of exactly that ending for the world. Time to roll it up. No more shall be saved on this particular planet.