I think the way Harry Connick Jnr handled it was very good. He didn't cut them down or abuse them, he just spelled out that it was totally not cool to be doing black face.

Australians do have the right to wear black face given there is no law against it, however they don't have the right not to be told that it is ridiculous, racist , and very offensive to a lot of people. Calling them a fuckwit, however appropriate, may be a step too far.