Has happened to me thrice in my 35 odd years (I am absent-minded). Never in an obvious form though. In each case the meat and veggie dishes looked similar.

In each case, it was a few bites (1-3... am not a very mindful eater; am usually reading or watching TV or talking), then sudden realization that something is off. Stop, double take, spit out into napkin, wash out mouth, feel nauseous for a minute, done. It's purely a physical reaction for me. I suffer no mental agonies like some people. Probably because my main reason for being vegetarian is that I was raised that way and am a creature of habit. Animal cruelty is a distant secondary concern and intellectual rather than visceral. Religion is not a factor.

I am not counting the cases where it is hard/impossible to tell (McDonalds fries, chips fried in lard, Hostess cupcakes with beef listed as an ingredient, soup made with chicken stock, Uncle Ben's rice, red food coloring made out of beetles(this is why I don't eat red velvet cake)...). Probably had a few dozen such cases. In each case I just stop eating the thing after learning about the stealth meat ingredient. This was all mostly in my early years in the US when I hadn't yet learned to be suspicious. no mental reaction other than the normal sense of having made a mistake. Like correcting a typo.

I am also not counting cross-contamination (any grilled veggie sub in the US is going to have some meat juices by virtue of being cooked on the same equipment). I try to avoid eating at such locations, but it is impractical to always do so.