A her is someone who was born with a vagina.

The very, very few people who don't fit clearly into either of these categories (intersex) are exceptions and can be handled on a case-by-case basis.

They are immutable because their reproductive role is immutable. A her can never impregnate. A him can never gestate.

(Either can choose not to perform their particular ability, or lose the ability to do so, but that doesn't change the meaning of these words.)