This feud has been covered in detail by Jeff Chang. The jist is that Banks is accusing Azalea of cultural appropriation (or "cultural smudging") and getting extremely emotional about, and Azalea is telling her to get lost in response. My reading is that most people don't have much sympathy for Azalea because of the way she seems to take a perverse delight in adding fuel to the fire, but at the same time, Banks has received a lot of criticism for claiming black "ownership" over hip-hop. Once art is out there, anyone can borrow it and be influenced by it, they say, although I can't help but wonder if these people were saying the same things when Katy Perry dressed up as a geisha.
Q-Tip chimed in with (naturally) a calm and reasoned approach to the whole controversy, saying that hip-hop can be fun but to never lose sight of the socio-political roots of the genre. The reactions of Banks and Q-Tip may be as genuine as they come, but they would sound ludicrous if they were talking about any other genre. Jazz and opera fans get ridiculed for assuming a self-righteous attitude about their music and setting up knowledge barriers for entry.
This stance is connected to hip-hop more than it is to race. Electro and EDM have crossed over into pop music, and they have their roots in black music as well. Nobody talks about cultural appropriation of those genres. Techno also started as a black socio-political movement -- disillusioned black kids re-imagining a decaying Detroit as a futuristic metropolis -- and despite its long history and rapid spread around the globe, anyone who tried to claim that you couldn't really understand it unless you came from Detroit would get laughed at. Techno always did a stellar job at incorporating its influences across racial divides though -- Kraftwerk and George Clinton stuck in an elevator and all that -- which helps to explain its global popularity.