The entire objective in acting is to perform as someone other than your actual self. One's roles should be limited only by one's talent—their ability to convince the audience that they are the character they are playing as. So, if they can pull it off, I have no problem with, say, a straight actor playing a gay character, a female playing a male, or even a little person playing a character of normal stature.
It is only when one acts as a mocking caricature that the performance becomes offensive. A white person playing a black character is not intrinsically racist, but blackface carries with it too much historical baggage to be acceptable. But when it is done with proper respect to both the art of acting and to the races and cultures represented, then I have no objection to actors playing as characters of other races, including whites playing blacks.
"Yeah, like how they're always getting Japanese guys to play Chinese characters."
On second thought, I take it all back. People should just be what they are. (Japanese playing Chinese? Burns me up so bad!)