I understand where you are coming from Lucy, but I think that (primarily because of the TRAs) the issue is much more complex than it once was.
Women (generalising here) have been allowing transwomen to share their safe spaces for decades, but this was effectively a courtesy which women extended to a group of people who they considered to be vulnerable and felt sympathy for - people who we perceived as being so deeply unhappy with their body that they were willing to go through incredibly invasive treatment and surgery to feel happier. We were told they were at risk of abuse and harm.
But the current tumblr generation, the hoards of TRAs, AGP men and the never ending expansion of the trans umbrella means that an increasing number of women don't feel that way anymore. Actually, I'll correct that - I think most do still feel very sympathetic towards the first group, the dysphoric transsexuals for want of a better expression.
Now we're faced with rapidly increasing numbers of people who demand access to women's spaces. Large proportions of them are not dysphoric, they don't feel the deep seated revulsion towards their bodies. Some are men with a fetish, some are good old misogynists, some are confused and misguided teens, some are abusive narcissists. Many aren't on hormone treatment and have had no surgery.
The courtesy we once willingly extended to one group is now being demanded by all under the umbrella, and whilst I think many who object would still like to extend the same courtesies to the original group we no longer can; because, at this stage, how can we tell the difference? It seems virtually impossible to create rules which will clearly distinguish between the groups.