Might not even be a cheese, but how it's prepared. I have a strong aversion (often triggering a gag reflex) with gooey/melted cheese, but almost any other consistency is fine.

Pizza, for example, I cook until the cheese is browned and no longer gooey.

It's so much easier to just say I don't like cheese than try to explain this to people. Too many will cook it gooey then tell me "this way it's not burnt"...