Ad hominem is incorrect. Ad hominem is when you reject a person’s argument because of who they are rather than the substance of the argument. This is them making a statement of their own, without presenting any actual evidence for it. (And Hitchen’s Razor applies here: the argument can be rejected outright due to a lack of any attempt to provide evidence.)

Sunk cost fallacy is wrong. To make it a sunk cost fallacy, the argument would have to have been something more like “you were born as a boy, everyone knows you as a boy, you have a whole wardrobe of men’s clothes, why would you want to give that up now?” As presented, it’s somewhat closer to a naturalistic fallacy.

False dichotomy is right, if we assume an unstated but implied “and therefore you can’t be a woman”.

False equivalence and non sequitur are absolutely spot on.

Skill issue just made me laugh 😆

“Trans people are mentally ill” is indeed a non sequitur, but if we investigate it a little further it’s even worse. If we assume an implied “and therefore they can’t know about themselves well enough to say they’re a woman/man”, it becomes a form of ad hominem, and begging the question besides. Ad hominem because “you’re mentally ill therefore can’t know the truth”, and begging the question because the underlying claim is “trans people aren’t real”. Why aren’t they real? “Because they’re mentally ill”. How do we know they’re mentally ill? “Because they identify as a gender other than the one they were assigned at birth.”