I was asked today which answer is correct: Me either or Me neither.
Let’s think about the choices. First of all, both are somewhat slangy. They are actually saying I don’t either and Neither do I.
If someone states a negative, such as I don’t like okra, the more common answer would be the one also containing a negative: Me neither. However, Me either isn’t going to make anyone tsk at you. But if the statement were I love (or hate) okra, your answer would probably be Me too.