Someone else in this discussion has pointed out that it makes sense that the Chinese is targeted at Chinese, as most English speaking folk don't know Chinese. And the English phrase is purposefully broad because English-speaking foreigners could be from a huge variety of countries.

Makes sense.

Still, wondering why the Chinese is purposefully so narrow and doesn't read '谢绝外国人‘ (no foreigners) instead of '谢绝中国人' (no Chinese people).

Leaves no room for misinterpretation, like we're already seeing in this thread.

A Chinese tourist, seeing a sign with unintelligible English plus "No foreigners" written in Hanzi/Kanji, could assume they're not foreign, since they're not Anglophone...

Correction: it reads '谢绝中国人' - made a typo when translating from traditional characters (which I use) to simplified.