Process theology developed explicitly as a critique of theistic personalism and classical theism's shared commitment to divine immutability and impassibility, arguing that a God incapable of being moved or changed by the world's suffering is, whatever its logical elegance, harder to reconcile with genuine divine love and responsiveness than a God who is; theistic personalists have generally answered that process theology, in revising immutability this far, ends up compromising divine sovereignty and perfection more than it gains in relational adequacy, since a God still becoming, still growing in experience, seems on classical terms to fall short of the complete, lacking-nothing perfection theism has traditionally ascribed to the divine.
The position sits closer to panentheism than to either strict pantheism or classical theism, since it wants God to genuinely include and be affected by the world's becoming, panentheism's core commitment, while still preserving some abstract, transcendent divine pole that keeps process theology from collapsing fully into pantheist identity between God and world. Eternalism poses the sharpest metaphysical challenge to process theology from outside theology altogether, since a block universe in which the future already, timelessly exists sits uneasily with process theology's central claim that the future is genuinely open and not yet decided even for God, which is why process theologians have generally sided with presentism, or some comparably open picture of time, over eternalism's completed block.