Kittens nails it, first post.
A woman is an adult human female who may look, behave, show likes and personality, choices, emotional skills, behaviours and lifestyle of any type she chooses. A woman comes in infinite variety. The only thing that every single one of them has in common is the biology.
That this is a very sad, hurtful, exclusive thing to some biological male people's perception is cause for sympathy, but this is the reality of the matter.
If in an attempt to be kind, we cover up and pretend that it isn't just that one fact of biology but some amorphous cloud of behaviours and choices and hairstyles and colour preferences so that males can be women too, (and completely women, transwoman as a phrase apparently isn't sufficient) then instantly a lot of women stop being classifiable as women, and yes, we very definitely risk imposing a singular, sexist and limiting idea of what a woman is, that harms biological females and throws their rights back about a century.
Is it really important to do this to all females so that a small percentage of males can have the exact, precise and unfortunately fictional label they would like?
Or would it be rational to expect those males to show some care and interest in the needs of the class of people they identify as and would like to be included in?
I still don't understand why TW isn't in itself an identity and classification of a group to be proud of. What is wrong with it? Biological female people cannot be TW. It would be beyond rude, inappropriate, assuming and disrespectful of biological females to identify as TW, which in reality they can never be. Why is it not recognised as equally disrespectful the other way around?
Should TW never be allowed support groups or specialist services that meet the needs specific to that group because it excludes female people or non trans males? Of course not.
The end game of trying to find a definition that removes biology however is to remove all single sex provisions from females specific to their group. Whether or not they need them, whether or not this leaves women without services, whether or not this makes things worse for 51% of the human race: this has to happen because males want it. Shared services, differentiated services, services that work for everyone and accept that 'woman' has different strands of need? No. Not allowed.
And there you see the intrinsic, toddler selfishness inherent in this misogynistic movement. Not inclusion but colonisation.