Well, three thoughts on that whole Situation. [spoiler]First, Khan Noonien Singh was Sikh, not Mexican, even if the actor first cast to play him was Mexican - it was the 60s, and they really only went as far as "brown's brown".
Second, in-story, I'd assume that him looking completely different was part of the John Harrison persona - if you're drafting History's Greatest Monster into your secret ops division and creating a fictional identity for him, it kinda makes sense you'd change his appearance dramatically while you're at it. You'd tell Hitler to shave if you don't want people to recognize him as Hitler. So it does kind of make sense that he wouldn't be Sikh.
Third, to quote the screenwriter, "Basically, as we went the casting process and we began honing in on the themes of the movie, it became uncomfortable for me to support demonizing anyone of color, particularly any one of middle eastern descent or anyone evoking that. One of the points of the movie is that we must be careful about the villain within US, not some other race." I can understand, and to a degree get behind, the not wanting to make another movie about The Evils Of Brown People.[/spoiler]
Fourth, Benedict Cumberbatch is really really good, pasty or no. This is no Last Airbender.