Lie #382 subsection 4 in the attempt to get women to just accept men in their single sex spaces already.
At least now we're moving on to the soft sell 'oooh look it's in your interest' batshittery, having given up on pushing the many previous lines that failed.
The straight forward answer to this one: look at the percentage of attacks on women taking place in gender neutral spaces compared to single sex.
So no.
You're welcome to have gender neutral spaces as well for those who prefer not to use the facilities of their (fixed, unchanging, factual) biological sex, but single sex spaces need to stay. And be exclusively for the use of that sex. (still a fact, based on fact and not personal preference.)
Because your right to wave your arms around any way you want ends at someone else's nose. Trying to persuade them that a broken nose is in their best interests so you can crack on doing your thing is frankly insane.