The problem there is metatextual: It would be offensive and unacceptable to cast a white actor to play a Sikh in and of itself.
Khan circa 1982
And this was the guy who played him in the 1960s.
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.
Um, also FYI Khan was said to maybe be an Indian Sikh in one episode back in the 1960s from an alternate 1990s where we had interstellar sleeper spaceships and parts of the Earth were ruled genetically engineered tyrants that was played by a man from Mexico.
Plus its been pointed out that Khan has a bit of a cultural mishmash thing going on what with not having the complete Indian Sikh look and Khan being a Mongolian tittle. So I can't really muster the outrage on this one.