This a case of one assuming God is a sky god. Christianity has always believed that God is a God who relates and who is personal. And whenever there is a personal relationship, there is a dynamic. And dynamics can involve both immutability and change. Whenever you have a personal dynamic, when one person changes, the other reponds in a way which reflects this change. But all is not relative.
If God's essence is immutable, then He is the standard by which such change is understood. For example, a man and a wife are in a happy marriage. The man commits adultery, and the wife becomes unhappy. Has the wife changed in a significant manner? Not really. Her change is a function of what her husband did, and reflects the immutability of her belief that infidelity is wrong. We have a set of Scriptures which speak of God's essence - it is unchangeable. The other set deal with God's relationships with men (they don't abstractly speak of God's essence). Thus, as the above analogies show, there need be no contradiction.