Medieval babies born with various detrimental intolerances, allergies, or just with some other congenital disorder would probably just not survive. But given the general mortality, it would sink into the statistics of the day of babies dying from (ordinary) malnutrition, accidents, disease or being-looked-at-funnily-by-that-old-woman-who-likes-cats[1]. And I doubt it there would have been much difference between the classes, when very young, and only those that survived long enough might be helped by the best doctoring that could be obtained by the parents.
Just like there'd probably have been roughly the same proportion of mentally disabled in the olden days as now, but the poor ones that could grow up to be a strong farmhand were tolerated as the hard-working village fool, and the rich ones were molly-coddled by their parents and may have made an attractive spouse if backed by loads of inherited/inheritable land, but the male ones may or may not have even continued their line (even if the wives bore 'heirs', if she was a smart lady).
Ahem, back to DF. There's a few challenges already coming in, regarding vampirism and the like, so right now I'm not too hot on allergies or expanding the syndromes still further, and I agree that dwarves are basically supposed to be tough little bleeders and not so easy to die, but as the game gets developed I could see something along these lines happening.
As to veganism? Beggers can't be choosers. Veganism is possible in a society (not necessarily a modern one) where non-meat options are at least not unimaginable. But veganism must necessarily also include "no wearing of leather armour", or using bone bolts. I can't see much opportunity in a standard fort (though the player could accommodate some of these things in their playing-style). However, I could see future dwarven preferences including various anti-preferences towards things like meat, bone, etc. Bad thoughts from being forced to eat a roast that (as at least one of its ingredients) contains some form of animal product (milk, cheese, the various meats and sweetbreads), or being forced to wear a uniform that includes a leather cloak/whatever. It might only go to the extent that they'd aim away from products they don't like (but use them if not available) or even completely stop them applying such uniforms and dying of hunger if all meals were meat-'contaminated'. But that'd latter would be down to a particularly extreme anti-preference.
[1] Who probably knew that the child was showing signs of lactose intolerance, being the bearer of knowledge passed down from other old women who were unofficially dealing with the health and well-being of those in the district. The ones that could intervene, explain something mumbo-jumpoish about spirits and successfully suggest some things that might help, at least. Getting blamed for the death was probably not a good thing, and survival was probably only possible if the married women of the district pestered their men-folk to leave alone the woman who had kept their babies healthy, and even (though they wouldn't openly admit it to the menfolk) provided pretty effective pre-emptive and reactive birth control measures (and assistance) to mature and young women, alike.