If we define hate by what it does, then we could easily answer this question by asking if God ever hurts people, if he ever hurts them badly, with no hope for redemption and no plan for ultimate good for them. Physically, we see God hurt people all throughout the Old Testament, and I don't mean Job, who was ultimately restored. We see him open up the ground to swallow some unauthorized priests. We see God hardening Pharaoh's heart just to give God a chance to really let him have it. We see him hating a tribe so much that merely killing all of the people isn't enough: he has to kill the livestock as well.
And we have people saying that God does not hate, but then, even for us New Testament folk we have the question of Hell. People are so averse to the idea of a God who hates, that they have made Hell into a sentient being of its own, a god beside God, against whom God will not compete. It created itself, or it went rogue from God's original purpose, and it swallows up people by the millions, and God is helpless to stop it. If, on the other hand, God gave it its fire, then God made it the everlasting torment that it is, and he willingly hurts people. If God has any means to stop people from going there, even one person, whether he appear to them in visions, or whether he simply removes Hell completely and replaces it with something less abysmal, and if God does not do it, then he hurts people in a way best described as hate. People comfort themselves against an angry God by painting him to be a weak one.
People see danger in the belief that God hates. If God hates, then they think that we will feel justified to hate, but that's exactly what makes our hatred unacceptable. We have not the authority of God, and we have no right to hate. Yet, those same people would take away God's right to hate. They may not bring themselves up to the level of godhood, but they bring God down to the level of a mere sinner. So, what harm does it do to believe that God does not hate if such is not the case? Simply stated, it causes us to follow after a God that does not exist. Moreso, it causes us to loathe God, who does exist.