Yank butting in here...
It's hard for me to see "blacking up" as relating to race. I always thought of it as chimney-sweep related, disguise-related. So no, it doesn't offend me -- on my behalf or anyone else's.

Good Soldier Schweik writes "Would anyone be offended if black dancers painted their faces white? "
Perhaps if white people had been slaves whose music was subsequently usurped by black people wearing white make-up at a time when white people were treated like second class citizens. Perhaps after that, some well-intentioned black person would be offended on behalf of the poor, voiceless whites and take it upon themselves to speak for them and demand the practice stop.