Does feeling hatred for someone achieve anything? Not by itself, that much is obvious. In addition to the list to assumptions that dot pointed out, I'd like to pose a few questions in counterpoint to some of the assumptions embedded in the questions. Does hate, or any other emotion need to accomplish anything? Why does hate, or any other emotion need to be justified by having a purpose? How does feeling hatred make you 'bad'?
I don't think emotions need to have a purpose, they just are, and despite our instinct to try and control them, it's enormously difficult to do so. It may be a bit easier to control our expressions of emotion, rather than emotions themselves, but the fact remains that we are not wholly rational creatures and our behaviour is often determined by how we feel rather than a rational interrogation of the consequences of our decisions. That's not a moral fault or failing, but is often treated as such. Emotional policing, and even emotional-self policing are mostly futile endeavours. I think Ted Kaczynski's writing about oversocialisation is instructive here, particularly the idea that setting a higher moral standard than can be achieved by individuals, and then denouncing or punishing them for failing to adhere to the unattainable moral standard is a powerful tool of social control, because they invoke guilt and shame which are both incredibly powerful and encourage self-policing. It's clear to see in religion and in the laws of the state. The point I'm trying to make is that requiring people to justify their emotions with a purpose, with achievement, is absurd when emotions, including hate, are emergent rather than intentional phenomena. The only purpose that can serve is an authoritarian purpose. An attempt to police emotion is even more egregious than an attempt to police thought, because it isn't just about controlling how we process and react to the world, it's also about controlling how we perceive the world.
"Does being violent against your percieved oppressors make you just as bad as them and not solve anything?"
It only makes you 'as bad as them' if you believe in an objective morality that everyone is accountable to. Furthermore there is a difference between violent conquest or aggression, and violent emancipation. Anything that increases my autonomy is desirable. Does it solve anything? That depends on the volume, intensity and persistence of the violence, along with a myriad of other factors. Violence isn't inherently morally wrong, and the success of violence is not dependant on whether it's 'right' or 'wrong'.
PS. Kudos for reframing the perennial 'is it okay to punch a nazi?' question in a more interesting way.