I'm going to accept Marvel's logic behind casting Tilda Swinton as The Ancient One

Marvel doesn't usually seem to shy away from diversity when it comes to casting their movies. Too bad they don't hire more women to work on said films, though. To be fair, it seems no one really hires women to do much of anything in Hollywood. You know what? Maybe it's just Paramount Pictures and 20th Century Fox. LOL, nah. It's all of Hollywood. If you don't belive me, go check out that thing I just posted about female directors, Fox and Parmount. Don't roll your eyes at me. I'm allowed to have opinions.

Also, Tilda Swinton can convincingly play anyone or anything, and we know this because we've seen her do it successfully time and again. If minorities were better represented in film, casting choices like this wouldn't be such a big deal to begin with.

DOCTOR STRANGE: MARVEL ISSUES STATEMENT ON ANCIENT ONE CASTING CONTROVERSY - ing.com