In an ideal world, it would be great to cast ethnicity by ethnicity. But with that said, Asian and Latino actors often have to compromise by playing roles outside their ethnicity but still within their racial group because there are so very few opportunities out there for minority-based roles.
With that said, I echo BillJ's point that Takei explained Sulu as pan-Asian. To sum up, we have a Korean-American playing someone with a Japanese first name and a Filipino surname. If anything these days, we're seeing more and more couples and families composed of different Asian ethnicities.