How does the church reconcile the immutability of god with the incarnation?
Actually, there is nothing to reconcile. God as God, does not change in that He has taken on a human nature—anymore that He changed by bringing about creation. Such change takes place outside of His Godhead. With the Incarnation, God took on a human nature. But the Son has always existed. As God, He did not change at all.
Fr. Vincent Serpa, O.P.