Jesus said, “My kingdom is not of this world. If it were, my servants would fight to prevent my arrest by the Jewish leaders. But now my kingdom is from another place.”
Christian leaders taking a hand in political affairs means they concerned about this world, which Jesus clearly said his kingdom was not a part of. In other words, their actions show they aren't a part of Jesus kingdom, but that of this world. Which... according to Matthew, currently belongs to Satan.
Which version of the Kingdom of God? The Kingdom of God went from an earthly domain to a spiritual domain depending what gospels you read. Jesus taught about a temporal kingdom of god tied in with his apocalyptic views, which is more evident in the earlier gospels. By the time John was written, it's something else entirely.