Does it matter? Even if trans people do not commit those activities at any different rate than others of their same sex... what will prevent non-trans-males from taking advantage of a law which allows self-declaration of gender identity with no requirement for diagnosis, treatment, or visible transition? What will prevent perfectly cis-heteronormative males from identifying as non-binary in order to gain access to those spaces?
What's to stop them from just walking in right now?
Right now, if a person who looks like a man walks in, the females in those spaces are allowed and empowered to speak up and ask them to leave, or to complain to management to remove them from the room. If a clearly male-bodied person comes into the shower, it is acceptable and completely justifiable for a female to react with worry and fear.
Sometimes we may choose not to make a deal of it, sometimes we might assess the situation and decide there's no worry. But we have the ability to object to the presence of a male in those spaces.
This changes that dynamic, in a significant way. This creates a situation where a female cannot object, cannot complain to management, cannot ask them to leave. Because all they need do is utter the magic words "I'm a transwoman". And any objection that a female has in that situation is now cast as her being a bigot and a transphobe.
Because gender identity, a completely internal and subjective feeling, trumps biological fact in these cases.
In countries where similar laws have passed, and similar social norms have been pushed, rape shelters and domestic violence refuges are being shut down and losing their funding.... because they refused admittance to a male-presenting person who claimed to be a transwoman. Despite the fact that females outnumber males by an immense margin in cases of rape and domestic violence, these shelters are now required to allow male-bodied people to stay their on their self-declaration. And if they don't comply, they get shut down, often they get threatened and vandalized as well. And those that do comply and allow self-declared transwomen in have seen multiple cases of completely inappropriate behavior - sexual solicitation, leering, and open masturbation.
Male-bodied people are being placed in female prison wings, despite their history of violence and assault, and despite their completely intact genitalia. The men's prison is viewed as dangerous to transwomen, and a cruel punishment because it doesn't affirm their gender. The answer then is to place those offenders in the women's prison, and apparently it's not considered cruel punishment to put females at increased risk of rape while confined against their will with a person of the opposite sex. The UK and Canada both have had multiple cases of transwomen inmates raping female inmates.
This act makes it so that areas where females would normally accept vulnerability, nudity, and exposure to other females must now allow males in as well. Because at the end of the day, there is no way at all to determine whether a person is a transwoman or a cisman.
