In other words, recognise that transgender is a category in its own right deserving of its own protections. Presumably no women’s groups would have an issue with this, but transgender groups would as they tend to equate gender with sex, and this relies on the concept of a legal sex
Transgender groups argue that separate provision for biological women and for people self declaring equates to discrimination and treating of self declared people as a different type of person, not as women. They see that as 'inequality' and 'lesser rights than other women'.
That is the part that has to be faced up to. Absolutely people should be able to believe whatever they want, live however they want, dress and present regardless of societal pressure around sex stereotypes and there is a strong case to provide resources and facilities for those who identify away from their biological sex for their privacy, dignity, safety and recognition of their choices. All fine. However biology is a fixed fact and you cannot allow males to identify into resources for the female sex without this heavily damaging women and removing their equality.
There is also the precedent here, that once it is fixed in law that personal choice must be accepted over material reality, other trans groups will want equal rights. So we will have trans aged and trans abled people who will want to be allowed to be 55 in a baby doll frock at your child's preschool, nappies changed on demand please, and trans abled people with carers and benefits and converted cars.... and that's just two already existing groups. How do you say yes to one and no to another? It won't be possible to argue it. Society can't set this precedent.
It HAS to be, full recognition of self ID - and trying to police 'living as' the opposite sex is ridiculous, it can't be done - and facilities provided in law separate to the facilities and resources for biological sex, but clear lines in law that biology is a fixed fact and in those few situations where female biology matters, transgendered people and biologically sexed people will be treated differently in order to meet and respect everyone's needs.
This will be argued against, but since that argument boils down to 'but women should lose their rights to give trans people what they want and it's just and worthwhile that they should', (ie the poster on here the other day saying they were prepared to accept a rise in assaults, exclusions and harm to women to provide full inclusion for trans people) it's not going to go well in the public eye. It's flat out sexism and as a pp laid out in their post, it's against a number of laws.