Now I'm fairly convinced you're not arguing in good faith, I'm afraid. This is a laughable analogy and easily disproven with quick googling of the organisation's scope and reputation, and by skimming the link I posted above of hundreds of examples of such organisations reducing women to bodily functions.
I'm afraid you're just not coming across as convincing when you perceive Millie Hill's witty words about this issue as poisonous "bile"... yet apparently avoid making any reference to CatsAreBetterThanMen's moving account of the physical and emotional harm that can be caused to women by the theft of their shared language and collective identity.
The contradiction here is similarly obvious in the posts dismissing women's concerns as "petty" and "unkind", and this issue as insignificant. The truth is that there is at least as strong an argument that transwomen claiming the words "women" and "female", and insisting on "she" instead of "they"/"zey" etc., is similarly "petty" and "unkind" and unnecessary. I'm interested as to where posters supporting the latter and condemning the former see the stark difference they appear to see - a difference so stark that it validates one as essential and the other as laughable or moral anathema - and whether they can articulate their reasoning.
Rhinos has done a great job of explaining our reasoning. Briefly put, if transwomen are women, then the people who are currently enslaved in Afghanistan and 70% more likely to be injured in a care accident in the UK due to their bodies, are left no word at all to name themselves and each other. In contrast, if transwomen are transwomen and transmen are transmen, then everyone has a word.
I'm just not seeing any argument from "the other side" that convincingly opposes this view - a view, after all, that acknowledges these competing needs, and considers how they can be addressed without one of these two groups being completely dissolved and silenced. I don't want transwomen/men to lose their identity, and I also don't want women to. The above - each having their own word, in a context of sensible acknowledgement of biological sex where required for everyone's health and safety - is my answer to this twisty mora dilemma. What's yours?
Because thus far, it seems to simply be that one group should defer to the other: "Silly women making a fuss about sacrificing or compromising their language!" and even positing arguments for retaining the original meaning of "woman" as irrational, hateful and extremist. Such extraordinarily emphatic dismissal of an entire demographic as being unjustified in even advocating for retaining its own descriptor can only ever serve as proof of just how much that demographic needs the language to advocate for themselves: of how devalued they currently are.
Meanwhile, beautifully expressed, step-by-step explanations of our (fairly straightforward) argument, supporting data (eg. Millie Hill's blog and transwomen's sexual offending) and intensely moving anecdotes (eg. my Black woman's Youtube vid. and Cats' daughter) seem to be being ignored, or sidestepped as too complex to address, or straight-up misrepresented. Seeing this happen quite honestly doesn't help to convince, either.