God used this historic empire to judge Israel and in fact Nebuchadnezzar it's king took many of the leading Jews captive back to Babylon where they lived for some seventy years. Babylon was eventually conquered by Cyrus the Persian (539 BC) who was kind to the Jews because he was working to build a multicultural kingdom therefore allowed the Jews to go back to their homeland in Israel. Some of this is recorded on the famous Cyrus Cylinder.
Many political leaders since that time have studied the model of Cyrus as an example to emulate. The weakness for Christians of course is that to put every culture on an equal plain there has to be some degree of compromise and evangelistic outreach becomes taboo.
Fast forward six hundred years or so and there is a cryptic illustration of Babylon in the Book of Revelation that was written by Apostle John while in prison a few decades after the crucifixion of Christ. It speaks of a powerfully seductive and wealthy nation or system that boasts of her glory as did ancient Babylon.
Everything must come to an end, and its fall is describe like this. “And he cried out with a mighty voice, saying, 'Fallen, fallen is Babylon the great! She has become a dwelling place of demons and a prison of every unclean spirit, and a prison of every unclean and hateful bird. For all the nations have drunk of the wine of the passion of her immorality, and the kings of the earth have committed acts of immorality with her, and the merchants of the earth have become rich by the wealth of her sensuality.” (Rev. 18:2)
I heard another voice from heaven, saying, “Come out of her, my people, so that you will not participate in her sins and receive of her plagues; for her sins have piled up as high as heaven, and God has remembered her iniquities. Pay her back even as she has paid, and give back to her double according to her deeds; in the cup which she has mixed, mix twice as much for her. To the degree that she glorified herself and lived sensuously, to the same degree give her torment and mourning; for she says in her heart, ‘I sit as a queen and I am not a widow, and will never see mourning.’ For this reason in one day her plagues will come, pestilence and mourning and famine, and she will be burned up with fire; for the Lord God who judges her is strong.
Many wonder how long it might be before America collapses in mire of its own moral decay. It is not like we can "come out of her" in the literal sense as did the early Pilgrims when they fled Britain. We might find ourselves having to separate from a religious group however that endorses ideas or theology that fly in the face of true Christian faith.