No normal guy wants a chick with a stick. If their sex isn't discernible, their pronouns are they and them, period. Normal (non mentally ill) people don't want to date sick people. **** them if their feelings get hurt. There, I said it.
What's odd is, in normal English, the last two uses of them and their are correct uses when referring to a single person.
What makes it absurd is, you have to use the singular they and them for a person - which can be confusing as hell, because when you use pronouns, it's implied the listener knows the one being referred to. They're placeholders. It can make language ridiculously cumbersome when you're talking about more than one person at a time. You might find yourself talking about a him - and then a her - and then a they but the they doesn't mean both the him and her but ANOTHER person - or maybe not.
STUPID. Just invent your own damned pronoun.
WORSE - because people are getting all pissy about it - YOU have to remember EVERY person's preferred pronoun. You can't just LOOK at a person and use he or she.
Then again - some of these people, you really can't figure it out at all.