The problem there is metatextual: It would be offensive and unacceptable to cast a white actor to play a Sikh in and of itself. There's far too much of a tendency in Hollywood already to cast white actors in roles that should be played by Asians -- The Last Airbender and Cloud Atlas have both drawn controversy for their choices in that regard. If we're supposed to believe that this is Khan's unaltered face, then that's just more racially insensitive casting, and Star Trek should be better than that. Assuming he got plastic surgery doesn't do much to make the casting more acceptable, but at least it's something.
For what it's worth, I have a good friend who is white, of Welsh-celtic extraction, and is a practising Sikh. It could be considered offensive to assume that all Sikhs are Asian.