Mildly, this isn’t be speciality, so hopefully someone else will come along.
I believe it is as follows. Our understanding of the complexities of the human anatomy is growing. As is our understanding of brain patterns and microbiology.
In terms of microbiology, there are differences between male and females values. People argue that it is the same for certain psychological traits. Notably, as everyone is unique, there will be a range for males and a range for females. I believe that some people are very keen to argue that some categories of males are approaching the female range in some areas.
However, that does not change the fact that a male who has gone through male puberty is irrevocably male, down to every single cell (possibly with the exception of sperm cells). It does not change the fact that archaeologist can differentiate between a male and a female skeleton.
It also does not change the fact that women need certain protections based on their biology as the only sex which gets pregnant and suffer from maternity related complications (need of adjusted work hours during pregnancy, protection against getting fired etc).
When it comes to the single sex spaces this does not have an impact either. A Muslim woman will not be able to remove her hijab if she is in a space where there are trans women. As for the pure safety aspect, many trans woman are lovely and need protection themselves. However, it is impossible to determine which trans women are lovely and which are predators. There is a conflict. This conflict needs to be discussed. And the easiest way to protect vulnerable women and children is to exclude all males.
I think many women here would be much more emphatic and keen to discuss solutions if SelfID wasn’t pushed so hard as was the concept that questioning anyone’s gender identity was actual violence. SelfID and no debate means that all males are allowed in every, disregarding legal protections, minorities and safety.