Honest question, how does this differ from a German or British actor playing an American, or vice versa?
For what I've seen, I'd say it's around the same, because for the most part Asian-Americans as a whole are still looking for stronger representation in Hollywood.
Past examples have run the gamut, usually depending on how rooted the role is in a specific cultural spot. Folks had issues with Zhang Ziyi as the lead in Memoirs of a Geisha, because that was a pretty Japanese story. In contrast, most don't seem as bothered by say, Randall Park (Korean) playing Louis Huang (Taiwanese) in Fresh Off The Boat, because hell, you have an all-Asian-American family on network TV.
Generally, it's the latter situation because as I said, Asian-American actors and actresses get so little play that everyone sort of grits their teeth and goes with it. There was an article about it somewhere around the internet.
You will run into native Japanese folk who will have an issue with it due to a very specific history between Korea and Japan.
EDIT: Here's one perspective, written by an Asian-American, using the example I actually gave before.
So when I saw that ABC sitcom Fresh Off The Boat cast well-known Korean-American actor Randall Park as the head of a Taiwanese American family, I felt unsettled by what seems like a persistent trend in Hollywood.
Seeing a Chinese man being played by someone who to me so clearly looked Korean made me uncomfortable because of the potentially dangerous message Hollywood is sending to the public: that all Asians are interchangeable with one another.
It implies ignorance of the centuries of history, hardships, and culture each country has built up over the years that are wholly distinct and unique.
Of course, every culture bears certain similarities, especially when those countries are geographically linked. But it's troubling to me that others might believe our identity doesn't matter in representation, supporting the stereotypes of squinty eyes and stinky lunches, without telling a specific story about a specific ethnicity immigrating to the US. It becomes cookie cutter, a representation of all Asian stories.
Don't get me wrong, I'm extremely pleased that there is finally a show on television portraying the Asian American experience. It's wonderful to see any person of color being cast in major leading roles. As a Chinese American myself, I was ecstatic to see people who look like me on the television who weren't relegated to play the token scientist or mystic sage.
I don't necessarily blame Park, or any Asian actor who takes these kinds of roles. Major roles written for any Asian ethnicity are few and far between, and actors must take what they can get. And perhaps the casting choice also represents a dearth of Chinese actors in America. All we can do is hope that the casting director at least tried to look for Chinese actors before looking at any other ethnicities.
But I can't speak for Asian-Americans. When it comes to black actors, we accept Idris Elba and John Boyega as African-American characters despite their being English because we still hold to some shared experience ethnically.