@Steve C. - I think it's a little different because white and non-white actors do not have the same level of opportunity - yes, there are a smattering of plays and musicals designed for a Non-White cast (almost always specifically Black/African-American - the only ones that come to mind as being designed specifically or Hispanic actors and actresses would be West Side Story and In the Heights, and the only ones specifically for actors/actresses of Asian descent I can think of are Flower Drum Song, Miss Saigon, and Allegiance). However the vast majority of works tend to have originally had all-white or primarily-white casts, so when you have a chance where a role doesn't specifically HAVE to be White, then one should be encouraged to cast a non-white actor or actress since otherwise they aren't going to have as many opportunities for roles as white actors and actresses. This doesn't necessarily mean you should enforce that the role should be non-white - talent should be the big thing you look for above all - but it should certainly be encouraged.
As for whether Hello, Dolly! can be considered a show that HAS to have an all-white cast, it certainly doesn't, as has been already proven by the fact that professional All-Black versions of the show have been done and were pulled off fine. Non-White people were around in Turn of the Century America, and as said by others, this is already such an idealized, fantasy version of Turn of the Century America that nothing is lost by Non-White actors or actresses being in the roles. I don't necessarily think the show should be lambasted or boycotted or anything by choosing to cast all or mostly white actors and actresses in the primary roles, as they certainly might have just happened to cast the most talented people who auditioned, but I can definitely understand why people are disappointed that such a big show isn't a little more diverse in its casting, since it's going to be guaranteed to give anyone in it exposure as people will be buying tickets by the boatload in the first place just to see Bette Midler on stage.