It is a well-worn cliche to attempt to separate the sin from the sinner, and to say that God hates the former, but loves the latter.
As with most cliches, there is an important measure of truth here. We can certainly say that God hates the sin, and yet loves them in the sense that he reaches out to the worst of sinners with the offer of grace and forgiveness.
But the cliche is still only a half-truth. In the words of William Temple:-
That is a shallow psychology which regards the sin as something merely separate from the sinner, which he can lay aside like a suit of clothes. My sin is the wrong direction of my will; and my will is just myself as far as I am active. If God hates the sin, what He hates is not an accretion attached to my real self; it is myself, as that self now exists.
In fact, we would be denying the witness of Scripture itself if were did not accept that there is an important sense in which God does indeed ‘hate the sinner’. True, the Bible more often speaks of God’s hostility towards sinful actions, than towards sinful people:-
First, there is the repeated statement that God loved Jacob but hated Esau (Mal. 1:2-3; Rom. 9:13). We should beware of reading too much into this given the question of the extent to which it is individuals or nations that are in mind, and the question of whether “hate” here is to be understood as in the injunction to hate one’s own relatives and one’s own life (Luke 14:26; cf. Matt. 10:37). Second, it is thrice stated that God hates evildoers (Psalm 5:5; 11:5; Prov. 6:16-19). Finally, God twice states that he hates Israel (Jer. 12:8; Hos. 9:15). Clearly these last affirmations do not preclude God’s love for Israel, as is proclaimed especially by Hosea. Perhaps we would remain closest to the emphasis of the Bible if we spoke of God’s hatred of sin and his wrath against sinners, though we cannot exclude talk of God’s wrath against sin or his hatred of sinners. A new slogan might be “God hates the sin and is angry with the sinner.”
Based on, and quoting from, this chapter by Tony Lane.
D.A. Carson (The Difficult Doctrine of the Love of God) offers a broadly similar account. Carson notes that in the first 50 Psalms alone, we are told that God ‘hates’ the sinner, or words to that effect.