I’m going to quote a previous answer, and I’ll tag it “crossethnic casting” for future reference. Ultimately, I think you should ask this question to Asian-Americans who are in the acting industry, because they’re the ones that are most affected and the most knowledgeable about the situation.
There are really two issues going on here, and I actually come down more on your side, but I understand the feelings of the other side as well.
White actors are generally not restricted by ethnicity. Take a movie like “Enemy at the Gates” where US citizens play Germans and British people play Russians and everyone speaks English. So on a practical level, I think that Asian-American actors face so many hurdles and problems in Hollywood, and have to scramble so hard to get anything better than a background ninja role, that I think we shouldn’t apply such high standards on them… higher and stricter than standards for white actors and white-passing actors.
On the other hand, Asians in English-language media are subject to the “all the same” stereotype in a way white people are not. People intuitively accept that white actors can switch ethnicities for movies and it doesn’t make Robert DeNiro any less Italian-American, for example. Asians have a long history of having our ethnicities erased, on the other hand, and told that they don’t matter, that we’re all the same, that we’re responsible for all the supposed crimes that anyone who “looks Asian” has committed.
There’s also the issue of inequality among Asian-American groups. We’re all underrepresented, but some of us are much more underrepresented than others, mainly Southeast Asians. As a Japanese-American, I don’t care at all that John Cho played Sulu, and neither did George Takei. I’m totally cool with it. However, if there’s a situation where Japanese- and Korean-American actors are taking jobs away from Southeast Asian actors who have an even harder time in the industry, then yes, there’s a problem there.
To further complicate the picture, there’s a huge career difference when it comes to Asian stars who got famous in their home languages coming over into English-language movies.
Overall, I’m OK with most Asian cross-ethnic casting, but I also understand why some people are really against it, and I empathize with them.