In regards to the world of acting, the whole [black/yellow/brown/red-face makes sense to me because it's just acting. If you want truly "authentic" representation, then you can find movies online. It would be nice if the "colour doesn't matter because it's acting" crowd be honest and state their double standard with coloured vs non-coloured characters getting a colour swap. Case in point about Cloud Atlas, people were crying about the yellowface, but I saw little outrage over negress Halle Berry donning brownface to play a Pajeet (?).
In the international theatre, characters are played by local actresses/actors and no one cares about being ethnically accurate. Plays inspired by historical figures like the Russian princess Anastasia or the Austrian empress Elisabeth (Sissi) have had productions in countries like Japan and Mexico and, since there's hardly any Slavs/Germanic actresses working there, they cast locals. Contrast that with usual American outrage over casting.