Does hatred justify violence?

No.

Violence cannot be justified.

Defense.

Violence is justified in many ways but never by hatred. You can drop a thermonuclear bomb on a city of eight million and justify it as you will but you can never say it was because you had hatred in your heart.

What @flutherother said. There are many ways to justify violence, defense being the main one, and even preemptive violence to prevent more violence (as in the case of Hiroshima) is justified by many, but violence as a response to hatred (or with hatred as the primary motive) is not justified.

IMO violence in self defense is justified.
Violence as a way to get your way is not. It may work in the short term but never in the long run.
Think of all the regimes that ruled with violence. They’ve all fallen or will fall.

Violence against Nazis is always justified.

No. The only justification for violence is when one has to react to violence.

Is it legally right to punch a Nazi? No.

Can you be arrested and fined or jailed for punching a Nazi? Yes.

Would I hold it against you if I were a hiring manager and I saw “arrested for simple battery – punched a Nazi in 2017” – on your resume? Hell no. Quite the contrary.