I cannot recall any instance in the United States when anybody thought I was anything other than a white person. Maybe, maybe there have been instances when people thought I was Latina, but since I can’t remember clearly, that means it has only happened rarely, and some people consider some Latinas to be white anyway.
So, when I was in Taiwan, it was rather surprising when some people assumed I was of partial east-Asian descent, or even fully of East Asian descent.
Usually, the latter only happened if they saw me from the back, and then they would be surprised when I turned around and they saw my face. However, I am astonished that I can pass as an East Asian even from the back. My hair, aside from being longer, is basically the same as my father’s hair was when he was my age. When he lived in Japan, women were fascinated with his hair because it was so different from the hair of Japanese people. It is the kind of hair which rarely occurs naturally in East Asian people.
The thing is, people alter their hair. Even in the United States, a lot of people are surprised to learn that, yes, my hair is naturally the way it is, I haven’t altered it beyond basic hair care. And people in East Asia also alter their hair. So maybe, when people in East Asia saw my back and my unusual hair, they assumed I was a local person who altered her hair rather than a foreigner whose hair is naturally like that – because they expected to see local people, not non-Asian people. Even though Taoyuan City – where I live – has a relatively large population of non-Asian people for a Taiwanese city, in any Taiwanese city which is not Taipei, non-Asian people are a rare sight.
(Fun fact: when I visited Kyoto, shortly after I moved out of Taoyuan, one of my reactions was: this city is full of white people! I don’t think I would have had that reaction if I had gone to Kyoto straight from the United States, or even Hong Kong. However, Kyoto has way more white people than Taipei, let alone any other Taiwanese city.)
When people actually see me, it’s pretty obvious that I have some non-East-Asian ancestry, and my speech makes it super-obvious that Mandarin is not my native language. Yet many people have assumed that I have an East Asian parent (usually Taiwanese, in encounters which happened in Taiwan) and are very surprised to learn that I do not. Apparently, it’s not just that they expect to see East Asian people in East Asia, it’s also that they do not expect non-Asians to be able to have conversations in Mandarin.
It’s kind of an odd way to see just how different the perceptions of people from a different society can be.
The Notes Which Do Not Fit 
People frequently think I’m half Japanese–it’s partly because of my field of study (what is a nice Latina doing studying Japan?) and partly that I look “racially ambiguous” enough that I guess I might look part-Japanese if you squint hard enough. (My mom is 100% Puerto Rican and has been mistaken for Chinese since she was a kid, so it’s not that surprising.)
I’ve heard from white colleagues studying China that they’re frequently assumed to be part-Chinese and to be fluent in the language when they go into the countryside (whereas they’re usually recognized as white and not assumed to be fluent when they’re in urban areas)–I don’t know if that’s been your experience, but I thought it was interesting, since I’m not sure I’ve had such a clear-cut experience in Japan.
What I have heard is that Beijing and Shanghai have a lot more white people than Taipei, and that second-tier Chinese cities generally have more white people than second-tier Taiwanese cities (beyond Hong Kong / Macau, I haven’t been to China, so I can’t say from personal experience). In fact, the people who are most shocked by the lack of white people in Taiwan are people who have recently travelled in China – “There are so many white people in China, why aren’t they here in Taipei?”
Even in Taipei, I mostly would not run into any other white people *unless* I was meeting someone or specifically going to a place where white people would be. And outside of Taipei, well, Taiwanese urban areas have just as few foreigners as the countryside. Actually, one is more likely to run into white people in, say, the rural eastern area of Taiwan than, say, Changhua City.