I do wonder if the "woman is entirely defined by gender and not biological characteristics" is a sincere belief of the trans activists, or if it's just a necessary adjunct of the intention to allow entire males to enter females personal spaces (in every sense of he word)
It's based on a line of thinking that has these premises:
- Sex is wholly separate from gender
- Gender is socially constructed
This means that there isn't anything innate in what makes someone a "man" or a "woman" but rather these are just constructed roles that people are socialised into performing. So a man is a person performing the "man" role. As this is socially constructed you can just reconstruct the role to remove any sex based requirements from the role. So a female can, by performing the social role, become a "man" while still remaining female.
I feel like this line of reasoning has become popular in some influential circles and by influencing social policy has come to a point where it's come crashing into traditional definitions where sex is a necessary part to these social roles.
Some have said that people need to experience gender dysphoria in order to really be trans, IIRC.
Bear in mind that this view, which would be considered "transmedicalist" today, has been the main view until at least 2012 where we started seeing arguments between "truscum" and "transtrenders", with the latter somehow winning out.