That is a good question. It's too bad the movie decided to use it to justify the casting. It didn't take the opportunity to explore identity politics.
Edit: Put a spoiler in my post.
Haven't not seen the movie I can't say how much they touched on identity politics, but from my perspective I worked on a cyberpunk video game which the inherent premise of the game was bodies were disposable and consciousness were interchangeable between sex and race. It wasn't really a character driven game so we didn't really dig into the premise of what truly is an identity if bodies are interchangeable but there's different room for it on film or a more character driven game.
I may ramble here but I guess my point is, even disregarding the
point I made above is there something inherent in her character that dictates she must be Asian?
I'm not attached to GITS in the slightest but it's an interesting social construct where someone like Superman is iconic and recognizable character associated as muscle bound Caucasian, black and blue eyes. There'd likely be a fairly big uproar (probably from myself included) if he was depicted on film as anything else.
Perry White is recast as black in Man of Steel? no big deal, his race isn't associated with his character.
Is Scarlett Johanson's character inherently Asian? to the point her
must be too?
For some, perhaps she is as iconicly Asian as Superman is Caucasian but I don't think she is globally or at least in the US.
Was there this much controversy with the 2013 remake of Old Boy with Josh Brolin? should their have been?