Brian Zahnd states he cannot believe in a mutable God in Sinners in the Hands of a Loving God:

The option of a mutating God who is in the process of learning and growing. I am not comfortable with this. The immutability of God is foundational to our faith. If God is subject to change, then the very ground beneath our feet is moving and nothing is stable. If God is evolving, how do we know that somewhere down the line God won’t mutate into an omnipotent malevolent monster… or something else? The idea of a mutating God is a radical departure from what the church fathers and Christian theologians, from Gregory of Nyssa to Thomas Aquinas, from Karl Barth to David Bentley Hart, have always said about God. Christian orthodoxy has always attested to the immutability of God. I cannot accept the heterodox idea that God changes.

Roy Kindelberger argues for perfect mutability in God’s Absence and the Charismatic Presence:

Fiddes rightly comments, “When we think at all carefully about it, suffering must involve being changed by something or someone outside oneself. It means being affected, conditioned and even afflicted by another. A suffering God must be ‘vulnerable’ in the strict sense of ‘open to being wounded.’” 21 Because the human Jesus was truly open to being wounded, so was God. If God suffers, and he does, then God changes; and if God changes, then he would be less than perfect if change was not internal to him. Scripture itself lays this foundation for the perfection and changeableness of God, so it is Scripture which leads us to conclude that God’s essential nature involves perfect changeableness. Jesus, Son of God, who once existed in one nature, now exists in two. Furthermore, this human God died a physical death and then added a further addition to the triune identity, an immortalized resurrection body.

Divine self-limitation of personal power was God’s decision regarding his relationship to the world, but changeableness itself is not God’s decision because it is intrinsic to him. When God’s perfect changeableness is expressed through the decision of self-limitation, the result is vulnerability, risk, and even suffering. God suffers because he chooses to open his perfect changeableness to the free experience of humanity, both as the God-human and by sharing our pain to the degree that it becomes his own. It is internal to God to suffer with those who suffer, “for we do not have a high priest who is unable to empathize with our weaknesses” (Heb 4: 15). Yet this suffering was the experience of God even before Jesus became our high priest. Prior to the creation, we simply don’t know what suffering God might have experienced. But once God introduced free creatures into his world, we can be certain he embraced their suffering and even rebellion as the “bearing” principal of an eternal God of longsuffering love. By his very nature, he bears the sin and suffering of the many. God can never be the same again, so he should be praised for the perfect changeableness he is.

Kindelberger, Roy D.. God’s Absence and the Charismatic Presence: Inquiries in Openness Theology (Kindle Locations 280-288). Wipf & Stock, an Imprint of Wipf and Stock Publishers. Kindle Edition.