Like anything it probably varies, especially by local culture. Source, method of production, smell, etc, as well as the particular product--there's significant variety to cheeses, not to mention dairy products generally. But one very general aspect described to me is the lingering milky mouth feel and aftertaste. That person didn't much like butter, either. I've enjoyed several East Asian analogs to cheese, like stinky tofu and natto; none are similar in that regard as they go down rather clean.

And don't discount the mental factor. I've eaten balut (the Vietnamese variety that is older and more developed), dog, live shrimp, fish gut soup, etc. Other than balut, which has a livery flavor (not to my personal taste, though it's more pronounced with duck than with chicken), the flavor and texture were never particularly foreign or distasteful, per se; the aversion was mostly mental and simply an artifact of cultural familiarity. The dog stew I ate was delicious, but near the bottom of the bowl, my appetite sated, disgust reared its head and I had trouble keeping it down. Later that day I learned my partner had the exact same experience. Fermenting and consuming the lactation secretions of herd animals is, on its face, kind of gross if it's not what you grew up with.

It's biological waste grown on cow extract. Pretty sure it's not that different from other gross-to-those-not-familiar-with-it foods, it's just that we're familiar with it.

An Asian friend once told me that when she came to America as a child and someone gave her cheese, she thought they were trying to poison her. I get the sense that that's not too far off from the common sentiment for those uninitiated.

East Asians have a higher rate of lactose intolerance.

I'd assume the mould is a deterrent.

Shoyu (soy sauce), sake, and miso are all made with mold (aspergillus oryzae) and are major components of Japanese cuisine, so no.

Shoyu and miso etc. are fermented, and the end result is all the consumer sees - the mould isn't there. My Japanese wife love all fermented Japanese food, but has an extreme aversion for mould of any kind, even in minuscule amounts. Her nose is hyper sensitive about the stuff. So no blue cheese here.. (she likes a lot of other types of cheese. She's not lactose intolerant, but in any case hard cheeses tend to be very low in lactose).

SE Asia uses mould too. Eg tempeh.