The issue of costume, actually, really doesn't apply on Halloween so much, because what makes this sort of thing offensive is about pretending to REALLY be something you are not (and especially about getting paid to do so.) On Halloween, EVERYONE is pretending to be something they are not, so the standard isn't nearly so high. (Of course, some costumes always come off in bad taste, so there is still a line; ethnic caricature should always be avoided.)
I think that the white face paint isn't nearly so much the issue, as is not using makeup to attempt to change the shape of her eyes. Make them dramatic, yes, but almond-shaped, no. The point is not to allow the portrayal to slide from costuming into caricature. (I also agree that the full white-face treatment might be a bit much for a child that age at a school event.)
The primary situations that get people up in arms about cultural "costuming" are those concerning paid actors. If a role calls for someone of a particular ethnicity, it *is* beyond insulting to hire someone of a different ethnicity and use makeup to try to fake it, when an actor of that ethnicity could have done the job. The latest situation of this sort was the casting of Emma Stone as a Eurasian woman in the film Aloha, but it first really caused controversy with the original casting of Miss Saigon, in which Welsh actor Jonathan Pryce was cast as the Eurasian pimp, the Engineer. (He was great in the role, true, but the Asian actors who have played the part since have also done very good work.) Some people will even take it back to Yul Brynner in the King and I, but Brynner actually WAS asian (he was of Russian Tatar descent)
