And if you understand the tweet, you'd understand the she was making fun of ditzy white girls who naively assume that white people can't get AIDS. It's a caricature of racism, not racism itself.
Personally, I disagree on both counts. I like offensive jokes of all kinds (I mean, if they're actually funny). Coming from a very homogeneous Central European country, I have never been on either side of oppression (other than being bullied in school for being weak, small, smart geek), so I definitely don't have your experience of being "hurt" by jokes, but your experience doesn't translate into a universally-applicable moral/rational argument that racist jokes are bad. However, even if I agreed with you and would personally dislike racist jokes, I would still strongly oppose restrictions or censorship on racist/offensive jokes, to avoid situations like the recent Charlie Hebdo attack.