unless it's obvious that those choices have been made as a result of ethnic privilege

I think the issue for some folks is one of representation
ie why get someone to play that ethnicity when there are a ton of people from that ethnicity who are just as qualified to play that role
This is especially a sore point when people of colour are replaced by white folk, because of the historical denial of our representation in popular culture
So I guess one way to see the Karate Kid casting is that Daniel being black is progressive in this light, while there's no need to mess with Mr Miyagi's ethnicity
(I personally don't think it's all that problematic since they're probably casting Jackie because he's a unique persona)

The other thing is that historically, Hollywood has treated us pretty generically
ie all Asians look the same to their eyes, so it doesn't really matter what ethnicity an actor is, just as long as they can wear a coolie hat and speak in broken english
So in this light, it's more than understandable that people are sensitive when Hollywood is like "oh it's ok, we'll just get a Chinese man to play a Japanese man" (not necessarily the case here), especially when you add in the factor that there have been inter-ethnic tensions between the two groups
Memoirs Of A Geisha comes in because there was a huge hubbub over the casting in that film (http://en.wikipedia.org/wiki/Memoirs_of_a_Geisha_(film)#Casting_controversy) dealing with some of these issues
Given that, it's perfectly natural to draw parallels between that casting situation and the one we're currently discussing