Gah. I knew I shouldn't oversimplify. By "category other people typically think of you as being in" I didn't mean their first impression based on the least smidgen of input; I meant their final judgment based on knowing all they need to know. If the lion's share of those people who routinely think you female only because the phone hides critical information about you would change their minds and think you male once they saw your face and your junk and your ultrasounds, that means you're in the "male" noun class. The "gender" social construct is not pig-headedly committed to first impressions.
Why should what group others think I'm in even be relevant?
Should?!? "There can be a gender to the mind" is an "is" claim, not an "ought" claim. Gender is determined by what others think, not by what the individual thinks. That's what "socially constructed"
means. There's a reason it has "social" in it's name: the same reason "socialism" has. If you aren't talking about how society categorizes something you aren't talking about a social construct, which means you aren't talking about gender. What's individually constructed in one person's mind is
gender identity; it isn't
gender.
If you're arguing what group others think you're in
shouldn't be relevant, that's not an argument for gender being up to the individual; it's an argument for abolishing gender altogether. We could do that -- we could simply stop basing any decisions on whether someone is a man or woman. But that would not make transwomen women.