A Calvinist explains the importance of immutability. From Wayne Grudem’s Systematic Theology:
f. The Importance of God’s Unchangeableness: At first it may not seem very important to us to affirm God’s unchangeableness. The idea is so abstract that we may not immediately realize its significance. But if we stop for a moment to imagine what it would be like if God could change, the importance of this doctrine becomes more clear. For example, if God could change (in his being, perfections, purposes, or promises), then any change would be either for the better or for the worse. But if God changed for the better, then he was not the best possible being when we first trusted him. And how could we be sure that he is the best possible being now? But if God could change for the worse (in his very being), then what kind of God might he become? Might he become, for instance, a little bit evil rather than wholly good? And if he could become a little bit evil, then how do we know he could not change to become largely evil—or wholly evil? And there would be not one thing we could do about it, for he is so much more powerful than we are. Thus, the idea that God could change leads to the horrible possibility that thousands of years from now we might come to live forever in a universe dominated by a wholly evil, omnipotent God. It is hard to imagine any thought more terrifying. How could we ever trust such a God who could change? How could we ever commit our lives to him?