If you are still around...
To deal with the points you raise...
'A seat at the table'. The problem is that women made what you might call 'reasonable accommodations' to transwomen, but then the piss started to be taken, with intact middle-aged men using female changing rooms, intact men getting themselves moved into the female prison estate and men (who even if they have suppressed their testosterone still have physical advantages over natal women) forcing their way into women's sports. Any attempt to say 'Er, hang on a minute, this doesn't seem terribly safe or fair...' was howled down with cries of 'TRANSPHOBE!' and 'NO DEBATE'.
Women who tried to discuss the issues on MN found themselves booted off the board (much gratitude for raising women's awareness is due to LangCleg and Barracker, both formerly of this parish, and others whose names I cannot now remember). Some women were hounded out of their jobs or sacked or lost work. A number of women left political parties (I was one of them) when they found that their reasonable questions were not answered and they were told to take a hike (I no longer vote LibDem at a national level, though I will locally for candidates I trust and whose views I know).
So, with that back story, they have lost any entitlement they might have ever had for 'a seat at the table'. They need to earn it back.
is there any science behind the claim that there must be something wrong with their minds? You might want to acquaint yourself with the paraphilia autogynephilia. I know you weren't talking about teenagers, but there is quite a lot of evidence that many of the young women caught up in this are autistic and often anxious, and thus vulnerable. I know of one who, in her late teens and after a grand total of three psych appointments, was put on testosterone and later had a double mastectomy - having been perhaps the most feminine of a group of sisters. As you can imagine, her mother is raging. It has been difficult for the siblings of the newly-minted transman; one has jumped on the beeeee kiiiind bandwagon, the other is a tactful but committed GC. No one talks about the fallout for the siblings...
You may have already had answers to your questions, but I've not had a chance to catch up today and I wanted to answer them since you had addressed me.