With all the other nonsense we accept in Trek, if people dislike this movie, don't go see it, or otherwise gripe just because of whether or not who is playing Khan is the "right" color or right "ethnicity," then Trek fandom has jumped the shark.
Besides, as has been said a dozen times, Khan is a Muslim title taken by a Sikh whose actual name is Noonien Singh. If one is comfortable with that contradiction, or can explain that away, then anyone should be able to explain away who plays the character just as well.
Also, a Dastar is a mandatory item of headwear for a Sikh male. Where's Singh's? If there's an explanation rationalizing why he doesn't wear it any more, then there's an explanation suitable for who's playing the character.
Further, to be most correct, Singh should be wearing a Kirpan. He didn't in "Space Seed", and he doesn't in STID. Maybe it was under his clothes. Maybe he doesn't wear it because Khan Noonien Singh doesn't seem to stand for what it symbolizes: peace, non-violence, defense of the weak, and truth.
There seem to be a lot of inaccuracies in the character to chew on and explain. So, why stop at the actor portraying him?
For one reason:
In order to chew on the inaccuracies you list one has to know something about the real world and about the cultures under discussion...
...whereas to complain about the actor playing him one only has to know about and have an obsessive concern with the trivia and minutiae of Star Trek.