> Their bodies, in an athletic context, are female.

I'm sorry, but this is not true. "Puberty blockers" do not complete suppress the effects of male genetics. They only attempt to block certain hormonal effects.

It is not possible to completely block the effects of having male genes by simple hormone modulation.

> Someone with androgen insensitivity can have XY chromosomes, yet be capable of giving birth

We do not determine eligibility for sports classes based on ability to give birth for good reason. It's not a proxy for the genetic athletic differences being addressed by these classes.

Individuals with androgen insensitivity typically cannot give birth. This an extremely rare possibility, not a typical feature of the condition.