In 1937, Vanguard Press published And to think that I saw it on Mulberry Street, by Dr Seuss, known to his family and friends as Theodore Seuss Geisel. The original edition referred to “a Chinaman”, which was later changed to “a Chinese man”. Chinaman is now seen as offensive though possibly not taboo, and no new children’s book would use it. As far as I can find, there are no direct equivalent instances of [Country] + man. The closest is Indiaman, but that didn’t/doesn’t refer to a person, but rather to a large ship engaged in trade between Europe and India. Dictionary.com notes that Chinaman was originally as neutral as Englishman and Irishman. The difference is that Chinaman is [Country]-noun + man (compare *Englandman and *Irelandman), while Englishman and Irishman are [Nationality]-adj + man (compare *Chineseman).
The Wikipedia article on Chinaman (linked above) mentions that Chinese uses 中國人 (zhōng-guó rén, China man/person), and I am familiar with Korean 중국 사람 (jung-guk sa-ram, China person). 중국 남자 (jung-guk nam-ja, China man) and 중국 여자 (jung-guk yeo-ja) are both also possible. I would not be surprised if many other languages use this formula. It is certainly not inherently racist. (Also, the Chinese word for a Western foreigner, 鬼佬 (gwei-lo), means ghost or devil man. Hmmm …)
A related use is a Chinese. For some reason, adjectives ending with –n, -i or –er can be used as nouns (an Australian, a Canadian (Canadia is a lovely place), a Pakistani (though one colleague referred to the Pakistanians in our college), an Iraqi, a New Zealander, ?a Britisher (apparently an Americanism, but I knew it first from the German characters in war comics) and the specialised use of an Afrikaner), but other nationality adjectives can’t (*a British, *a Swiss). Note that some countries have a noun to refer to the person (a Briton, a Spaniard, a Finn, an Aussie (also an Aussie person)). Some countries are awkward in any case: ?a Burkina Fason (apparently Burkinese), ?a Côte d’Ivoirean (apparently Ivorian). I added a Maldivian and a Nuiean and then found that they are actually used.
Less is said about the rajah in Mulberry Street. Depicting a rich person from a country with a long (albeit mostly difficult) historical relationship with Europe, specifically Great Britain, is apparently less offensive than a standard (or poor) person from a really exotic (at the time) country. (Wikipedia’s article on Geisel says that he and his wife had travelled extensively by the time he wrote Mulberry Street, but it doesn’t say where.)
Alongside Seuss’s words are his images. In the original edition, the Chinese man was distinctly yellow and had a pigtail. The question in my mind is: when does any depiction of any culture, especially one other than the artist’s own, become racist? Indeed, when does a depiction of the artist’s own culture become racist? Any depiction of any culture must include distinctive, typical, even stereotypical features, otherwise there’s nothing to show that it’s that culture rather than any other culture. Take a moment to search for “image Chinese person” and “image cartoon Chinese person”, or your own country/nationality/culture, for example. If Dr Seuss was/is racist, then so are most of those artists.
There are no doubt some images which are accurate and sensitive and are intended to promote understanding or even admiration. There are equally no doubt other images which are inaccurate and insensitive (deliberately or accidentally) and are intended to ridicule, demean or promote fear or hatred. (Geisel produced a number of propaganda cartoons during World War 2.) Where is the line, who gets to decide and will any amount of ceasing publication or banning result in any benefit to anyone directly affected? I don’t know, obviously. If you clicked on this post looking for an answer, sorry.
All of this is complicated by the processes of pejoration (where favoured or neutral terms become disfavoured or taboo), amelioration (where taboo or disfavoured terms become neutral or favoured) and reappropriation (where (some) members of a group reclaim a taboo or disfavoured term for themselves).
And to think that I saw it on Mulberry Street is, ultimately, a book about the importance of imagination and the greater importance of distinguishing imagination from reality and telling the truth.
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Never Pure and Rarely Simple 
Regarding the identification of nonwhite people, it is noteworthy that while “black” and “brown” (with the former now usually capitalized) are encouraged, “yellow” is still not acceptable to refer to those of East Asian descent. (The various geography-based terms are generally inaccurate, but that’s worthy of a separate discussion.) It’s also notable that “colo[u]red people” is considered offensive but “people of colo[u]r” is approved.
A few years ago in the US state of Alabama’s Senatorial election, candidate Roy Moore (who was controversial for all sorts of reasons) received flak for a comment that referred to groups of people by their color. He defended himself by pointing out that he was merely taking the terminology from the popular Christian song “Jesus loves the little children of the world” (red and yellow, black and white…).
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Disclaimer: Anglo/Saxon/Celtic/Aussie, if you haven’t figured that already.
I wasn’t consciously aware of b/Brown, but reading about it, I spotted an exchange between Steve Biko and a judge which I remembered from the movie Cry Freedom, who asked ‘Why do you call yourself black? You’re more brown than black.’ Biko replied ‘Why do you call yourself white? You’re more pink than white.’
Recently I have read references to both George Floyd and Meghan Markle as b/Black, which makes me wonder what the word actually means.
Searching for ‘image Chinese/Japanese/Korean people’ shows that their ranges of skin tones are pretty close to Caucasians – the difference is more in facial features than skin tones. Whatever colour Indigenous Americans are, it’s not red, but then red hair and red wine are not really red either.
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