IMO Eddie Murphy and Arsenio Hall "whiting up" in "Coming To America" is the funniest part of the film. I understand that other white people may find it offensive, but this white person would find it objectionable if the opinions of other white people were allowed to spoil his enjoyment of films like that.
When it comes to "blacking up", the problem is there's a history associated with it. If, nowadays, the blacking up is in the same spirit as the whiting up above then I don't see a problem with it; if it's harking back to the historical mockery then there is a problem, obviously. If all blacking up is verboten because of the history, then that history lives on in creating division and tension; it has to be allowed in the right context.