I think it hasn't aged as well because in large part, the world grew up a bit in the meantime. Most of us look at that movie, see the obvious racism, and cringe because that's no longer part of the social norms we find acceptable.
Racism was not acceptable in 1991 either, but the films running point: that no matter how much time passes (for Kirk from TV to film) racism (creeping or overt) stills informs perceptions, no matter how rational the troubled person is in every other situation.
Adding to that, general "social norms" today accept racism more today than in 1991: from post 9/11 racism on a multi country scale which still runs strong, to the increasing level of general racism online (example: read the comments on any Yahoo news story dealing with African Americans in some political or social sense) and promoted by race-baiting stories (see: Fox News, talk radio, etc.), racism is not only the leading story almost every week, but its big business like never before.
It could only remain so strong because of a willing audience, the feeling that through tools such as social media, anonymity allows the power to be as outrageously racist without a single fear of exposure or consequence. As a result, the culture comes to expect it from every corner. If anything, the racism in TUC (especially politically motivated) is more relevant today than in 1991.