Firstly, as Khan is a product of genetic engineering, he needn't belong to any one particular naturally-occurring race (or even combination thereof) at all. McGivers was only "guessing" (her own words in the episode) at his origins in "Space Seed." And moreover, Montalban was neither Indian nor Sikh, illustrating readily that the race of the actor playing a role needn't be taken as a direct indication of the race of the character himself. (John Cho and Linda Park aren't Japanese, either.)
Secondly, we could easily regard any discrepancy among Khan's appearances in TOS, TWOK, and the new film as being no more significant than that of any other character who's been played by more than one actor, including Saavik, T'Pau, Braxton, Pike, and many others. In other words, not significant at all, because it's not an "in-universe" difference, merely an effect of recasting the role, an aesthetic choice on the part of the people behind the camera, which we of course notice on our end, but which will not be acknowledged by the characters and which we are intended to look past.