So if I understand your point correctly, it's not about having a responsibility to the culture, it's about having a responsibility to the message? I'm not religious, but I listen to some religious music without feeling bad because what the lyrics are communicating aren't leaving an impression on me.
Yes I think the article is saying that if you're a white fan of black music (specifically the music where they share their stories of struggle and pain) and the messages of that music leaves no impression on you... then that's odd, and deserves some inspection.
That's sort of the point, yeah. It's not that white people have a responsibility to agree with the message of black rap, it's that white rap fans have a responsibility to not be ignorant of black struggles. The issue is that white rap fans don't seem to care about black people and are truly ignorant of their struggles, almost as if they revere the "coolness" of rap, but don't think black voices have any importance.