I've found that the reaction to the word "moist" is highly dependent on the context. For example, a cupcake described as moist sparks a feeling of deliciousness, while some potting soil described as moist gives me a sense of completeness or stability (plants typically need moist soil to grow, so it's a good thing). However, a bus seat described as moist triggers a feeling of revulsion.
Sorta, it's also a mental image thing and a visceral reaction. Like fear of clowns or trypophobia, there are valid reasons for the visceral reaction (being moist in certain situations can be quit4 uncomfortable and in some rare situations causes at least minor irritation or injury), but usually don't apply for most circumstances. Clowns aren't dead people, and most bunch of tiny holes aren't insects or disease... well, maybe a lot of them are insects.
Visceral reactions are uncontrollable, so while it may be propped up a lot as a joke on the internet, I think it's a bit condescending to assume something that doesn't bother you doesn't actually bother some people for real.
Yeah, generally people like to take a small issue and blow it out of proportion. I've always liked Pineapple on Pizza, but I know some people who can't stand any sweet and salty mix. Similarly, I don't like coconut in sweet stuff, but I love it on its own and love it in savory foods.
I've definitely talked to women irl who dislike the word moist, from friends, coworkers, and family members. I don't recall any men getting disgusted with it irl, (except from that one meme) though I can imagine some uncomfortable situations (moist socks, moist undergarments, etc).