When I was growing up in the MS Delta, I attended a segregation academy for one year (Indianola Academy). All other schools I attended in the Delta were strongly majority-Black (mainly because most Whites could afford to send their kids to a segregation academy).
There were mixed-race kids in the public schools, and without exception, they were accepted by the Black community, but not by the White community. Yes, there are some in the Black community who aren’t comfortable with biracial people (remember when some were saying that Obama wasn’t Black enough?), but in my experience, such are very much the exception to the rule.
When it comes to Asians (in Asia, though to a lesser extent in America), however, the dynamic is different. In my experience, it’s less about being “Asian” than about “which part of Asia are you from”. It’s as if there is no real sense of an “Asian” race, but of Chinese or Japanese or Indian or Indonesian or Filipino. Racism in Asia is, well, expected and even understood, and so is not a normal part of social discourse.