This is a link to Maria Miller's Transgender Equality paper for those who haven't seen it
It is well worth a read as not only is it broadly the basis for this entire thread, but has been passed to the govt for consideration for ratification into law. What is in this report is absolutely real and could be law very soon.
I fully support the rights of transgender people to live peacefully and free from oppression and discrimination. I don't believe this should happen by taking hard fought for rights away from biological women.
I also think that the insistence that trans people are exactly the same as biological women/men is disingenuous in the extreme. I don't want to hurt anyone's feelings or infringe on anyone's rights to exist peacefully, but there are a great many medical conditions that are sex dependant. There is no such thing as female prostate cancer or male ovarian cancer. At some point in their lives, in order to remain biologically healthy, almost all trans people will have to acknowledge their biological sex.
Pretending this isn't so does the trans community no favours whatsoever. And the skewing of statistics around biological sex affects epidemiology which then potentially affects the entire population in terms of health research and resource planning.
And to pretend sex differences don't matter is also disingenuous from a safety perspective. I don't believe trans people are all potential rapists because that's utterly ludicrous. However, I do believe that there are many predatory men out there who will take advantage of a law that says that the only modification men need to make in order to access protected women only spaces is to open their mouths and say "I identify as female". That is all they will need to do. And some men will do that - of this I have no doubt whatsoever.
I get the reticence of some posters about entering into a debate that might feel transphobic or go against the accepted social narrative around inclusion, but honestly, as a society we need to have a critical and open debate about this on all sides so that we can move forward safely and equitably as a society. Otherwise we are sleepwalking into a situation where women and trans people are at risk of harm.