When the actor for Khan of the original timeline was not Indian either? In 'Space Seed', he was said to be North Indian and probably Sikh; and Khan himself acknowledged the painting of him wearing a turban.
Yet he did not look like a North Indian Punjabi, and he spoke with a Mexican accent. He was nothing like an Indian.
This isn't what people are complaining about. They are complaining that Benedict Cumberbatch is a pasty-white Brit, while Ricardo Montalban was, well, Ricardo Montalban, just because it was never made 100% clear that Khan was genetically altered to look different. If a dark-complected Mexican was cast as Khan in STID, nobody would be complaining (or at least no one who needs to be spoon-fed every detail because they can't work things out for themselves.)
And as for your point: Lots of actors play ethnic roles of which they do not belong. In Hollywood, if a Middle Eastern character is needed, one does not get the role just by being Middle Eastern, one gets the role by being a good actor who can pull off being Middle Eastern.