Divine Immutability is one of the hallmarks attendant with classical theism’s theology proper (i.e. doctrine of God). If someone denies this hallmark, according to the orthodoxy of classical theism, that person is not to be considered orthodox; instead, heterodox, or even a heretic. There are many classical theists, particularly in the classically Reformed quadrants who see Karl Barth as an outright heretic; typically for an array of uninformed reasons, based upon the received caricatures (in that tribe) of his theology. Be that as it may, when it comes to immutability in Barth’s theology, what we get is not its rejection, but instead, its reification and reformulation (which is true of Barth’s overall project in regard to the retooling of the traditional categories). For Barth, his ‘retooling’ project is a function of his adoption (and development) of an ‘actualist’ theological ontology; it is through this ontology that the orthodox loci become subject to an amplification vis-à-vis their circumscription by God in Christ (through Barth’s basic—to his theologizing—doctrine of election).
In the following we will see how Barth’s actualism retains the classical doctrine of immutability, but within a genuinely Christ-event[uating] frame; as that is narrated for us in the Apostolic Deposit left for us in the New Testament (as that is given prolepsis in the Old Testament). Sumner writes, at some length:
To relativize notions of becoming according to the nature of divine eternity is not inconsistent with the medieval doctors. Where Barth is most original is in his rejection of a metaphysic of being that precedes act, and in its place his desire to form theological judgments according to the gospel as an event. As we see in Chapter 3, this actualist approach includes a rejection of any distinction between God’s being and act, or His essence and existence, so that God is His activity—He is “the living God.” A description of this activity inevitably implicates God’s covenant relation to creatures, so that “God is” means “God loves”: God has caused His being to correspond to the covenant. Insofar as it relates to time and change, this ontology is patterned by the dialectic of an eternal promise (to become incarnate in Christ) and its historical fulfillment (the birth of God’s Son in Bethlehem).
A consequence of this ontology is that the issue of divine immutability is placed into a very different light. On the one hand, the being of God is neither prior to nor distinct from God’s act (logically or ontologically); and on the other, God’s protological decision in election is the more determinative of the dialectical poles. Historicization is the accomplishing of a reality that, for God, is already the case. Bruce McCormack is therefore right to argue that the Son is eternally human in the mode of anticipation (Logos incarnandus), and in time in the mode of historical actualization (Logos incarnatus). The solution to the dilemma of immutability is therefore evident: the Son does not change in the incarnation because His assumption of human essence is an eternal act. He has, in a sense, always been human.
One obvious objection must be immediately met. The suggestion that Jesus Christ is eternally human appears to collapse time into eternity and negate the historicity of the incarnation, robbing the virgin birth in the stable of Bethlehem of its import as the moment of becoming. Jesus effectively brings his humanity with him from heaven, according to this objection, and that Annunciation and Christmas stories are a sort of narrative falsehood—not the Word’s birth as a human but only His transmigration from the heavenly realm to Judea. The way in which Barth has related the incarnation to eternity, however, should make it clear that it is not the case that Jesus brings his humanity with him. As the Son of God he is eternally human only in the sense that: (1) he is present to all temporal moments at once; and (2) he is the Logos incarnandus, the Word who is to become flesh in time, and therefore human strictly in his readiness for God’s eternal covenant designs to be fulfilled among creatures. He no more brings his humanity with him than God hands down to Israel its entirely completed and fulfilled covenant and asks nothing further of them. The point of the actualist account is not that Christ’s humanity is uncreated (it is not) but that the divine person who is Jesus Christ is uncreated—that is, the anti-Arian doctrine of Christ’s preexistence. He would bring his humanity with him from heaven only if it were actualized in eternity, and not in time at all. But creation is the proper sphere of its actualization, the sphere of God’s redemptive work in fulfillment of the covenant, and the place where the Son of God is born (though not begotten).
Such is the argument for divine immutability that is suggested by Barth’s actualism—and, if we were to accept his revised ontology, this much might leave us satisfied. It is a clever solution to an ancient theological problem. But if we were to stop here we would not be doing full justice to Barth. Much of this argument, as I have said, is simply implied by Barth’s work. What he says more explicitly, however, indicates that we have not yet gone far enough. . . .
As we leave off with Darren, we can see that he has more to say in regard to Barth’s fuller treatment in this area. But suffice it for our purposes to leave off where we do, as Barth’s reification of immutability through his actualist theological ontology is given definition.
It is this theological ontology that has transformed things for me, personally. Some want to label Barth’s actualist ‘being-in-becoming’ ontology as existentialism; but it’s not. Instead, Barth’s theological ontology is in fact: dialectical. Barth doesn’t absolutize existence as a prius to essence, instead he thinks these two realities together (but not without distinction) through the novum of the hypostatic union in the incarnation of God in Jesus Christ. This is what it means to think God as event; to think God from His Self-revelation in the humanity of the Son made flesh, while at the same time understanding this Revelation as genuinely revealing the reality that God has always already chosen to be for us, from Himself.
Divine immutability is retained in this ‘Barthian’ frame just as humanity is not foreign to God’s being, but one that He has freely chosen for Himself in the Son’s election. The distinction between Deus incarnandus and Deus incarnatus helps to recognize how this Subject-in-distinction dialectically identifies how it is that God can be ‘unchanging’ while at the same time becoming, as the eternal reality of God’s anticipation to become human, actually, eventuates historically in the incarnation. We can see how this maintains the Creator/creature distinction, while at the same time providing for a continuity between God’s being and becoming in the enfleshment; insofar as the being is not in itself contingent upon the becoming (i.e. temporality)—in fact it is just the inverse: the becoming is the being in ‘downward’ motion, consistent with who God eternally is in the humiliation of the Son vis-à-vis the Father.
I wonder if this has clarified anything for you (reader) … do tell.
 Darren O. Sumner, Karl Barth and the Incarnation: Christology and the Humility of God (New York/London: Bloomsbury T&T Clark, 2016), Loc. 5261, 5269, 5277, 5284, 5292 Kindle edition.