My tastes often pertain to the food's texture. I don't particularly like mushrooms, due to the texture. Bell peppers, again due to texture and a bit due to taste. Eggs need to be cooked properly, else they will make me sick. I like dippy eggs (under-cooked yolk), but the egg white needs to be fully-cooked. If there is any trace of slime, it makes me sick, and it feels like snot.
I had an allergic reaction to king crab legs at a Chinese buffet, once. My hands became red and puffy, and so did around my mouth. Though, I'm not sure if that was due to the crab, or due to what it was cooked in. I usually don't have a problem with shellfish.