Apart from rap just, really, really not at all being anywhere in the same ballpark, there are examples where rap music has undergone social scrutiny and changed as a result: Cop killing lyrics. I'm not saying they don't occur at all any more, but they're considered much less acceptable than in the 90's.
Maybe I've lost the line of thinking here. I thought we were talking about black face, and why people are offended by it. It's an offensive racial stereotype. I really don't see anything comparable about thugs. I'm not even clear on what you mean by thug outrage: is it that thugs exist? Is it media portrayal of thugs? Is it that thugs do or say bad things? I am honestly confused by this comparison.
My point is that "gangsta" rap music is every bit as offensive as blackface, perhaps even more. But outrage culture selectively applies the "harmful" argument to the latter, not the former. Nor do they make as a big deal of it.
Thanks for clarifying, I see where you're coming from now.
Between blackface and gangsta rap, there is a difference in kind: Black face is emblematic of society itself continuing the practice of dehumanizing a group of people that historically were dehumanized and stripped of all freedom. Gangsta rap represents something that is not nearly as systemic.
That's somewhat beside the point though. You touch on a relevant question: Even if many fewer people are offended, they are still offended. So the question is, should society not urge any action at all for offensive speech? Should no one feel any pressure to modify their behavior in some way? If you don't want to go to those extremes, then you have to draw the line somewhere. Currently society draws the line at racist content, specifically that aimed at traditionally downtrodden minority groups, and even more specifically, those minority groups that still experience significant bias.
Why does society draw the line where it does? My guess is because the scars there are not completely healed over, even if society has "recognized the error of its way". On other stereotypes we aren't as adamant. Irish, for example. We don't view the drunken Irishman stereotype with quite the same shock, probably in part because the institutionalized oppression (In the US) has been mostly dead and buried for a 100 years. In the UK & Australia however, the wounds are more fresh, and reference to derogatory Irish stereotypes are much more taboo.