The Stoic doctrine of apathes/apatheia is flatly denied by the Christian tradition wherever the latter asserts God's free involvement in the world. Moltmann is right when he says that we cannot read the passion narratives and conclude that God is aloof and unaffected by us. While some ancient and medieval Christian writers evidences a wariness towards attributing emotion to God, at least in etymological terms God's impassibility referred not to an inability to relate or to feel, but an inability to suffer. ...
If we say that God is not intrinsically affected by the world, what are we to make of the intimacy of that personal relationship that God is represented as having with his creatures? Yet if we say that God is intrinsically affected by the world, how can we continue to say that God is perfect and independent of created reality? The answer proposed here is to recognize that although God exists independently of creation, he freely chooses to enter into a genuine relationship with the world. In this freedom for creaturely reality, God is genuinely affected, although in any given case this is to be understood in an analogical rather than a univocal sense. ... [Michael S. Horton, Lord and Servant: A Covenant Christology (Louisville, KY: WJKP, 2005), 42-3]
Impassibility, or the doctrine of a God without passions, is highly controversial in the modern world. From the liberal (small 'l') side, Jurgen Moltmann is the most well known for promoting the suffering of God in his book The Crucified God. Open Theism has been a Trojan horse for bringing this nonsense into the so-called Evangelical camp, while the Reformed Baptists have been having some problems with the issue too it seems.
Of course, part of the confusion over impassibility lies with its definition. What do we mean when we say that God is impassible, that He has "no passions"? Does it mean that God has totally no emotions like a robot or a rock? Most assuredly not, so what exactly does impassibility mean?
Impassibility is a corollary to immutability. Immutability is the doctrine that God doesn't change. Impassibility therefore is the doctrine that God doesn't change in His emotions. In other words, God's emotions are self-determined and steadfast. It is we who change relative to God, not God Himself.
It is here that I would like to demur from Dr. Horton's portrayal of impassibility. According to this (earlier) book, impassibility is to be seen more along the lines of the non-suffering of God. God is dynamically involved with the world, though it is because God freely chose to interact with the world, and such dynamism is to be understood analogically. This however to me is the wrong way to go about understanding impassibility, which seems to me to be better understood as God's steadfastness in regards to His emotions, i.e. immutable with regards to His emotions.
Perhaps in an effort to simplify the issue, the question to be asked is this: Can a creature cause God to feel a certain way? Or to use stronger and more intensive language, can the creature emotionally manipulate God's emotions? If one were to (correctly) deny that the creature can ever cause a change in God's emotions, then what kind of dynamic quality and genuine affecting can we claim for the creature with the true God? But if all emotions in God are self-caused and independent of the creature, can we have a true dynamism in this relationship? Now of course God does relate to His creatures especially Man, but since God is Lord, it seems that the "dynamic" interaction must be due to us not to God. In other words, God's emotions are constant and steadfast, but it is we who change, thus resulting in the illusion of God's "changing" emotions towards us.
When we read that God repents, we are to read it as an anthropopathism signaling not that God actually repents in the essence of His being, but that God seems to be repenting because of the changes in people and the environment. To unrepentant sinners, God is constantly in a emotional state of wrath. To the elect who has repented and turned to Christ for salvation, God is constantly loving us in Christ. To the believer who continues in a state of sin, God is grieved over this sin and disciplines His children for our good. In all this, it is not God who changes, but Man. God is constant and thus unchanging (immutable). He always has wrath for the unrepentant sinner, always has love for the elect who repents and have faith, and always grieves over the sin of a believer in sin.
This understanding of impassibility as self-determinance and steadfastness seems to be a better portrayal of the God who is steadfast (אֱמֶת - emet) with loving kindness (חֶסֶד - hesed) towards His people (e.g. Ps. 25:10). It is not the Greek Stoic ideal of apatheia, but it does contain the idea of unchangeableness like it. This, as opposed to Horton's (at least) earlier portrayal of impassibility, seem to be much more biblical.