Transwomen are not normally fertile, since the hormone treatments seriously impede the working of their testicles (if they still have them).

One would assume surgery or hormones are required to change your gender designation in Washington State, but in fact this is not the case (neither is required). Here's the form to change gender designation on your driver's license in WA, anyone living in washington state can do it today: https://www.dol.wa.gov/forms/520043.pdf

Will that lower insurance rates? Hmm...

It's all about 'gender identity' these days, not hormones and surgery.

Indeed, in trans circles, expecting the latter as a required factor is often considered highly offensive. This, and the notion that a person needs to experience gender dysphoria to be trans, is now derisively known as the 'truscum' point of view.

I think the vast majority of binary trans people consider gender expression to be an integral part of gender identity, and at least a majority also consider HRT or surgery to be a significant component. I think there are close to 0 people walking around with a beard and wearing masculine suits that identify as transwomen.

Non-binary people are another discussion, and how they should fit into male/female spaces is of course unclear.

Overall, I would agree that prison assignment should depend on more than reported identity. Especially since it is conceivable that people in prison are likelier to lie about their internal identity if they believe they can get something out of this lie. This is much less relevant for lower risk environments, such as bathrooms (in my country at least, unisex bathrooms are anyway quite common) or gym lockers.