Because Julie's story pivots on ''passing,'' it's reasonable to say that the actress playing her (Caucasian or light-skinned black), can pass for white.
However, this is no way analogous to the ''Miss Saigon'' situation. Jonathan Pryce wasn't hired because he could pass for Eurasian (or else he wouldn't have worn prosthetics to make his eyes more ''slanted'' in London). More importantly, I've never heard of another instance where a show tried to defend its casting of a white actor in part because it claimed that no actors of color were capable of the role. And to add insult to injury, we find out that the show even lied about making a worldwide search for one. Frank Rich, Dick Cavett, George Will, etc., were outraged that a white actor might be denied a role, but where's their outrage about all the male Asian performers who were unfairly accused for lacking the talent?
Which brings me back to my main point: Why has yellowface been acceptable (on Broadway and movies) in a way blackface is not?
I'd love to hear more thoughts about that, but I guess some folks are more interested in debating whether ''yellowface'' takes quotation marks.