Right now, you’re able to select the appropriate gender marker on your passport without a note from a medical professional (and a passport can be used in the vast majority of situations you’d use a birth certificate) but because the self select gender marker was done by executive action, it’s extremely likely to be reversed when Trump takes office.
Also, having one might be a good idea in general.
This sounds like exactly the type of thing they’ll reverse, either through executive action or pushing through the GOP Congress and Supreme Court. If you can afford it, go for the full US passport.
Let them reverse it then. That is no reason to not get one now.