If you mean that those identities can't coexist in one person, I don't think you are right. There is an idea of possible worlds (suggested by Leibnitz) which in one of its reading says that a person lives in different possible worlds: in one he is a father, in the second he is a teacher, in the third he is a son, in the fourth he is a husband, in the fifth he is a customer, in the sixth he is a lover etc. These epitomes don't exist simultaneously, one of them surfaces at a given moment (say, when you are spending time with your kids your are a father), while others "stand by". When you come to the office you stop being a father and your CEO epitome switches on. Curiously, different epitomes can be axiologically different - one may be a good CEO, but a bad father, a pleasant customer, but a horrible husband.
If we adopt this approach, the different identities you speak of may not be mutually exclusive - one can be a patriotic feministic nerd who is a connoisseur in pervert games.
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