the problem is that asians are not interchangeable. it's not like having a white girl play another white girl. race, ethnicity, and nationalities are not the same thing.
there is a deep-rooted issue in people thinking and saying all asians look alike even if they're from different cultures and cultural backgrounds. it would be one thing for a chinese pb to be raised by koreans (due to the character still being chinese), but just saying a korean IS chinese is inherently racist, because it implies all asians look alike, it doesn't matter their background, you can just sub in one for another and call it a day.
both characters from mulan are chinese (with mulan being rooted in real chinese storytelling), so yes, people would glance and sideeye ignoring that and the fact there are plenty of chinese performers and figures to use for their child. not doing so is both ignorant and lazy.