She was a sworn Kingsguard to Renly Baratheon. She watched him get murdered by a shadow right before her very eyes. She was then blamed for said murder and the guards tried to have her killed. What would have happened if she died? It would have mattered naught to Stannis. He was butchering his brother and to hell with the fallout. That isn't just.
Stannis is entirely responsible for this chain of events.
Of course she is justified in her quest for revenge. If we're considering revenge a just cause at all. I think you're taking things to a meta level that doesn't begin to appreciate or recognise personal connections and conflict.
Sure, it hardly matters in the "context of the universe" but then almost the entirety of the plot and character interactions don't matter in that sense either. It matters to Brienne and that's what's relevant in this whole mess.
And said oath is 1) no longer necessary as Renly is dead, and 2) false anyway, as Renly was never the King. It's not Stannis' fault that she was blamed for Renly's death. What would have happened had she died? Unknown, and not relevant. As well, he was entirely just in sanctioning Renly's death: Renly was a usurper trying to steal Stannis' rightful and legal inheritance, and was threatening to kill him to do so. Stannis' had to do something. Killing Renly was the only just action that could have abounded. Renly deserved it. Stannis was doing his duty. Renly was being selfish.
No, she's not justified at all. She's supporting a man who was never King, even after his death (and her subsequent allegiance to another dynasty which she acknowledges is illegal). In this case, her revenge is unjust. Her seeking revenge was never just. I'm taking things to a level that doesn't account for those, because those ideas of personal conflict and connection have no place (and should have no place) or relevance in the context of legality and justness. Her loving Renly does not make Stannis a bad man for killing him. Her inability to see Renly's own unjustness (usurping a crown meant for his brother) is at the core of this issue as well. How is she being just for supporting an unjust man?
Especially since she's breaking her oath to Catelyn (and to Jaime) to protect and watch over Sansa (who still lives) to take her unjust revenge. It's not making her sympathetic. It makes the name of her sword an irony.