I think Jae's tired / there's a bit of a typo.
Longterm vegetarians LACK the enzymes to digest animal proteins, sugars, and lipids. Because they don't have the enzymes to digest them, they make the person violently ill. Sometimes for 'just' a few hours, sometimes for several days. ((New vegetarians, and most V kids still produce the enzymes to greater or lesser extent, and pescatarians -just seafood-, and those who intentionally consume some meat products (like vegetarian except for bacon) or like bouillon or weekly meat, purely to keep their enzymes up can eat meat or food that's gotten meat on it, without getting ill... because they still have the enzymes)).
Then there's the moral aspect. I consider it this way; I don't eat dog. I would not eat (unless I'm starving) any dish that has dog in it, even if half of it was 'dog-free'.
Now I'm NOT a vegetarian... My husband (and about half my friends) are vegetarian (of varying kinds). Their answers as to whether or not they'd eat from the same dish vary based on how long they've been vegetarian (aka will it make them sick from the "meat cooties"), and how they feel morally about eating meat.