It’s not pseudoscientific jargon. Sex is not pseudoscience. And sex based behavioural differences/neurological processing isn’t either e.g. this recent study out of Oxford.

If what makes culture is our collective behaviour, and sex influences those behaviours, then gender as a product of culture is still a product of sex differences.

We can play with words all we want, but ultimately ‘woman’ generally means ‘sexually signals as an adult human female’ - trans-women who have transitioned physically do end up as women according to that definition, but people who assert they simply feel like women and do not need to attempt to sexually signal as a woman to be so need another definition of being a woman.

So the question then becomes if we don’t identify a woman as someone who is sexually signalling as an adult human female, then what do we identify a woman as?