If you are one of those fortunate people who has never struggled with self-hatred, you may find this topic outside of your experience and might consider skipping it. But if you know the struggle, maybe take a walk with me through some thoughts on the topic.
I think "Is it a sin?" can be the wrong question. First, if "too much self-condemnation" is the problem, then "even more self-condemnation" cannot be the answer. The question is more about how to exit the turmoil inside when thoughts of self-hatred come along -- and cling like burs in the spring-time.
Because of the place of love and forgiveness in God's judgment, I see self-hatred as against God's will; and yet not everything that is against God's will falls under the category of "sin." If we look at the world to come as a guide to things that are fully God's will, then the world to come has no death or illness -- but these things are not sinful themselves; it is not a sin to be sick or die. Mourning has no place in the world to come, but for today, "Blessed are those who mourn, for they will be comforted."
And there is a kind of intentional self-hatred that I expect is a sin. If I see a train of thought starting and turn my thoughts against myself by design, if I set about self-hatred willingly, I have no doubt this is wrong, and in a way for which I'm responsible.
But self-hatred can also be a form of spiritual malnutrition: if we lack experience of acceptance and love, if we have not seen a mistake met with compassion and understanding, then we may need more spiritual tools and spiritual growth before we have the ability to respond with compassion and understanding.
Condemnation and accusation are among the tools of evil. One of Satan's titles is "the accuser." So there are times when self-accusation and self-hatred are the front lines of a spiritual battle. (I'm not usually one to talk of "spiritual battles." That phrase has unfortunately picked up common usage in settings where every thought is dramatized in a way that loses my patience. Still, there are certain times where certain things feel like battles, and for me this is one of them.) So it may be more useful to think of self-hatred as something of a spiritual battle, one where nobody has handed me the spiritual tools or training to fend off that attack, and yet it can be done. It can be more helpful to think of arming up with the Lord's tools for the fight: truth, faith, righteousness and the like.
Coming back to the point about spiritual malnutrition, it can be helpful for the spiritually starving to be guided to faith, hope, and love. These are found in Christ, found in the confidence that we have value in the eyes of God, which brought Christ to fight for us. The Scriptures are full of reminders of our value in the eyes of God, of the shepherd looking for the sheep, of the woman who would not stop looking til she found what she had lost, the father who would not give up hope that one day his lost son would return, ready to welcome and celebrate.
Those who preach God's love for us, they feed the sheep.