Should I be offended?

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People were laughing at the character and not at black people.
Othello was black & Hamlet white. Would you like to see Cassius Clay played by Vinnie Jones or a KKK Grand Wizard played by Will Smith?

To be honest, I can't imagine wanting to see a film featuring either of those characters...

But I'd happily see, eg Adrian Lester* play Hamlet. If you can do it in modern dress, which you can perfectly well, why not ignore race? Othello is trickier, because there will be specific references in the text to his colour, but a skillfull production will get over that. Hamlet was also Danish, but that didn't stop Olivier playing him in the high RP accent of the time. Theatre (and by expansion, all drama) is fluid and artistic, and if the production is good, it can be innovative - although innovative for innovative's sake is not always a good idea.

*in fact, checking the facts, I find he has, to acclaim. He's also played Henry V and oh, yes, Rosalind in As You Like it.