And, really, we should be in an "advanced" enough society that doesn't tolerate such parodies and caricatures. I go back to my black-face reference above. If a movie was made today with white men playing black men using black face and other offensive features common to turn-of-the-(last)century performances (big, red lips, monkey/ape-like features people would call it offensive and would rightfully protest the movie.
Humour is a tricky thing. You are always going to risk offending some people. Last night during the Oscars, I saw William Shatner, dressed as Captain Kirk, make a black-face joke and a gay joke (both at the expense of the host). I then saw a talking toy bear named Ted take the stage and make jokes about Jewish people owning Hollywood. These jokes were told to an audience of an estimated 1 billion people. We may be a technologically "advanced" society, but we aren't quite at the 24th Century level of tolerance just yet.
As for white men playing black men in movies, Robert Downey Jr. was nominated for the Academy Award in 2008 for his portrayal of "Lazarus" - a white man who dyed his skin to look black - in the comedy "Tropic Thunder".