Friend:  I don't understand why anyone feels like they can even police this.
Me: Is there any real way to police these things? Not really. But it makes them feel morally better because they're "protecting the women and children" from the perverts.
They use scare tactics to try to portray it as protecting women from the scary transexuals that are going to rape them. This is one of the few issues where conservatives and radical feminists have come together on an issue, and so these types of attacks have come from both sides over the years.
A quote from a feminist book from the 70s:
“All transsexuals rape women’s bodies by reducing the real female form to an artifact, appropriating this body for themselves…Transsexuals merely cut off the most obvious means of invading women, so that they seem non-invasive.”
Yes. Obviously transwomen go through all they go through just so they can get close to women in secret and rape them. And yes, radical feminism(aka Gender-Critical feminism, or TERFS) is still alive and well today.
There has been an effort to police gender expression and gender identity going on for many years, this is just their latest tactic as they lose other ways to do it.
(an interesting read if you want: https://theestablishment.co/the-lefts-long-history-of-transphobia-288ec857c09c#.dls1lpkrr)