As someone who is also mixed, I can say that there is a reason why people like us are "over-serious" about race. When you grow up getting asked what your ethnicity is before someone even asks for your name, it can be an issue. When people constantly make stereotypes, or place you in the "oh, you're not like the rest of them!" camp, it becomes a problem. I can understand Tahan's point of view completely... and I can see why Mikkayla's comments bother her, because they also bother me. I get that Mikkayla hates being pointed out that she's asian over and over - it's annoying - but she does go a little too far with the taking the mick out of stereotypes. There's a point where you cross the funny line, and I think she probably does from time-to-time.
The interesting part is that Mikkayla was actually BORN in Korea, so she actually does have a real connection to Asia besides her actual ethnicity. I can see her being the type who was raised very far away from the notion of remembering your roots as I've met lots of people who behave the same way she does and had the same experience growing up. At the same time, maybe it's her way of coping with some racist remarks. Either way, I wouldn't give Mikkayla a hard time but Tahan is allowed to get annoyed as a fellow Asian. Tahan doesn't really fit any stereotypes of her own background, so you can see she's spent much of her time fighting them. I am the same way.