This is a mistaken understanding of the law of identity. It does not say that something can be only A or B but nothing else: it says that something is A or not-A. So in the case you gave, it does not say that something is either 100% an uneaten apple, or it is not an apple at all. It says that whatever the entity is, that's what it is.
If it is a brand-new uneaten apple, then that is what it is (and it is therefore not an eaten apple). If it is a half-gnawed apple, then that is what it is (and it is therefore not an uneaten apple nor yet an apple core).
I've heard the argument also given like this: "Aristotle says that you are either/or, like you're either drunk or sober. But clearly you can be slightly buzzed, which is neither drunk nor sober, so I have proved Aristotle was wrong! Damn Western logic."
Aristotle, of course, never said that something cannot exhibit partial characteristics (as, for instance, an adolescent may have some properties of an adult, and some of a child, without having the least bit less identity because of it).
PS: First post! I found this forum about a week ago and have been very impressed with the level of rationality on it. Don't know if I will ever get to 1000 like some of the regulars.