I don't (and I get the impression that most of the people who have posted in this thread don't either) really give a damn about them casting a black actress as Hermione. While there are points in the book where Hermione is implied to be Caucasian (at one point saying that her face had gone "white with shock," IIRC,) being Caucasian isn't an integral part of Hermione's character. I mean, in the UK edition there is no particular description of Dean Thomas (it's only in the US edition that he's described as a black Londoner,) but seeing Alfie Enoch playing him in the films didn't evoke any negative reaction from me at all. It's not like Dean (or Hermione) adhered to some some bizarre racial stereotype.
What does bother me is the possibility that they specifically chose to cast Noma Dumezweni, not because she's an excellent actress who's won an Olivier Award, but because the colour of her skin would cause controversy and bring more publicity to the production. That just leaves a sour taste in my mouth.
Actually, this kinds of makes me think of an episode of a short-lived sitcom called "Ed," starring Tom Cavanagh (J.D from Scrubs's brother.) The episode in question had a guy who was running the school play being sued by a kids parents because he purposely refused to give the lead to their kid, due to him being black.
Sounds like an open and shut discrimination case, until you find out the play is about Abraham Lincoln, the American Civil War, and freeing the slaves.
Historical dramas, and media where race is an integral part of the plot, are the only occasions where skin colour should be a factor in casting choices. Casting a black person as Abraham Lincoln strays far too close, IMO, to censoring history to attempt to minimise or play down the historical wrong-doings that did occur, and should be remembered (if not obsessed over as some do.)
But when it's not? Then it shouldn't matter. It's like, when there was all that controversy about Michael B Jordan playing Johnny Storm in last year's Fantastic Four movie. The only way it would have been a problem for me is if the character he played wasn't recognisably Johnny Storm (and, you know, if the movie sucked, which it did.)