I'm from India and this is anecdotal, but I've never met a person who's intolerant to dairy. I heard about lactose intolerance only after moving to the US. In most part of India, dairy is an integral part of diet.
I first heard of lactose intolerance when my son became lactose intolerant at age 1.5. I also discovered then that the pharmacies were stocked with lactose-free milk substitutes (soy milk was comparatively harder to get hold of). They'd apparently been stocking this stuff for years.
More surprising, the first time I heard of a nut allergy was when a friend (around the same age as yours truly, born sometime in the decade of The Emergency) said he had one.
Milk and its byproducts have been a revered part of Indian religious traditions from ancient times and hence the source of consideration behind the cow as a holy symbol