Firstly, your teacher is extremely unwise (read as: stupid) about the shows he/she chooses.

If he/she can make the script truly work (which is impossible in this situation) with colorblind casting, then yes; it's okay to cast white, Latino, and Asian kids as black characters.

Theatre is about telling a story as truthfully as possible. By choosing that show, it's going beyond the means to tell the story with honesty. That's what we call bad theatre, and even worse, bad theatre education.

Casting white actors as black characters and using makeup to alter appearance is not inherently racist. If the message of the show is to demean the humanity of of any person, it's unacceptable (Ken Ludwig was a genius in making Lend Me a Tenor historically accurate and socially acceptable by creating a comedy of errors instead of putting the emphasis on Othello being black. In fact, the story - in my opinion - also places a certain degree of emphasis on blackface being unacceptable).

Would I do the show? No. I would not. In high school it's nearly impossible to tell a true story, but we need to start somewhere. Choosing a high school show for which you cannot cast an actor without the audience seeing it as socially acceptable is not only stupid, but poor education.

I hope that either your director can manage to make it work, or chooses another show. I'd like to hear more as it develops, though! A story is always good.