I'm sure there are lots of other things in wine that people are allergic to. However sulphites are one of the top allergens, which is why they are included in mandatory labeling laws.
I don't particularly enjoy not being able to eat almost all dried fruit, and having to watch everything I eat. However I enjoy painful rashes on my tongue even less.
Yes allergies and sensitivities are vastly over diagnosed, and also underdiagnosed. However as there's no definitive way to diagnose allergies it's impossible to state how many people are allergic to anything. Even if it's just the placebo effect it's better than nothing.
Get a really good potato masher -I find the ones that are a thick wire in a wave shape far superior to the grid style mashers.
Then if its not mashed enough use a hand mixer with beaters or if the potatoes are needing a gentle touch try the dough hook attachment.
If you have one of the hand powered food processors it might work as well