I don't necessarily agree with but do have sympathy with IW and with those who would term themselves as the 'old school transsexuals'. When it was simply a case of a very small number of the population who were for the most part gay males and had made a full physical transition, there were all the same issues for female people including major ethical ones, but the impact was small enough and quiet enough in approach to female people that they were for the most part able to have that use of female spaces. For a time it more or less worked if you didn't look too closely at the issues.
This ship has sailed due to the political lobby. IW like Debbie Hayton, would like access to women's spaces restricted only to males who have made enough of a transition - Willoughby has explained in interviews, Willoughby doesn't want to use mixed sex spaces or to share with those Willoughby themselves perceives as males. To them it is about protecting the full sense of transition and entry to women's spaces for themselves, so they can feel themselves as a woman amongst women. However from the female perspective, as the quiet bits got very loud indeed and it became obvious that the slightly opened door of any male permitted at all was going to be forced to its widest extent of all males wishing to feel themselves as a woman among women regardless of motive being admitted, with a side order of gleeful enjoyment in silencing, oppressing and excluding non compliant women, and a whole lot of 'there's no such thing as sex but a woman can have a penis' and how impossible it will be to have any boundaries at all.... it's shifted to the only possible line being no male people at all, ever, regardless of circumstance.
Third spaces are the only remaining solution. IW doesn't want third spaces, for the same reason that a self identified male with a beard who is gender fluid doesn't want third spaces: the presence of women in those spaces to be among them is essential for feeling validated. However the real need for safety, privacy, dignity, respect for chosen TW identity, has to be separated from any male person using female people, many of whom don't consent, because it validates them. Which means not equally respecting female people's safety, privacy, dignity and respect for their identity, plus excluding those females who can't do it from having any space at all, for the better happiness and sense of self of a male. That's the bit that is unacceptable.
Sadly, to IW and many others, that's the bit that is really painful.