State trooper makes a traffic stop. Compares the driver's ID to the driver. It's not clear to me how "Male, but Femme" or "A dude, might be wearing a dress today" is any more helpful to the cop than "Male".
In fact, I'm hard pressed to think of *any* scenario where it's helpful to me, or to society, to know what gender a person thinks themselves to be.
ETA: Okay, thought of one. If you're a mental health professional considering a diagnosis of gender dysphoria, and accompanying treatment plan, then yes, it's helpful to society to know what your patient is thinking, gender-wise.
On the other hand, society has deemed gender identification to be unhelpful in certain situations. Hiring. Renting or selling a house. Things like that, noticing or caring about someone's gender self-ID is unhelpful.
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And can you imagine Amber Alerts, for example? "Red Toyota Corolla, [LIC], driver is a white male, but be advised he thinks of himself as a woman."
Or even worse: "Driver is a white male, be advised he also identifies as a white male."