> † To the best of my knowledge, there is no significant amount of lactose in cheese. But it is still a good indicator that milk features in the culture.
Lactose content depends on the kind of cheese. As a rule of thumb, the longer your cheese is matured, the less lactose remains.
But the maybe 38% of Italians who can digest lactose ( https://pubmed.ncbi.nlm.nih.gov/28673071/ ) still dwarf the ~7% of Chinese who can. If your only exposure to whites was Italians, with their very strong cultural features of cheese†, cream-based sauces, and ice cream‡, you'd still know that (1) whites consume much, much, much more dairy than Chinese do; and (2) they are much less likely to suffer any negative consequences from doing so. On the other hand, Italians would probably sympathize with the risk of indigestion from drinking milk "wrong" where Danes or Dutchmen would most likely just be confused at the idea.
My white ancestry is mostly drawn from England, Ireland, Sweden, and Russia, so the baseline expectation for me to be able to digest lactose would be a lot higher than the Italian baseline. Visually I do look more like a southern European.
† To the best of my knowledge, there is no significant amount of lactose in cheese. But it is still a good indicator that milk features in the culture.
‡ Ice cream is also very popular among the native Chinese.