I guess my question would be: to what extent does it matter? There is no real benefit, as far as I am aware, to claiming that you identify as a woman after being arrested; the penalty is the same regardless. Is there going to be an organized campaign to rape women, claim a non-cis gender identification and skew the statistics? If not, it's going to have no tangible effect.
To take an example: racial identification is largely self-reported. It's entirely possible, for example, for those arrested for sex crimes to all identify as Polynesian, which would skew crime stats. Is there a large public outcry about this possibility? No. Because it's just not a thing, just as this is not a thing.
That's where the transphobia comes into play. Causing a major fuss over something that has zero real world impact in order to attempt to erode the societal standing of a group of people that actually exist and are already marginalized.
I think it matters to a lot of women.
All those women who believe that they need a single sex safe space in certain circumstances are scared enough that the term woman now applies to anybody who chooses to use it, like its a badge that could be taken on and off at will. Women's refuges or female only changing rooms should not be taken from women who feel they need them, yet they will be...
Any person who believes that sex and gender are different things will be concerned because it effectively means that single sex segregation cannot happen because Trans rights trump biological women's rights and if you disagree then you're a TERF or a transphobe.
Anybody that believes science is a thing, and that evidence is important will be concerned because while it is easy to accept that some people don't feel that they are the gender assigned at birth, it doesn't make any logical sense that everybody else has to believe it too in the face of all evidence...however failure to pretend that you do believe it makes you a transphobe.
Importantly, I don't think that this situation will cause there to be a rash of sex crimes carried out by trans sex criminals, however it opens almost every single female space to abuse by anybody that wants to gain access, who can then use self identification as a justification for entry to a previously denied area.
In terms of the headline, that was about recording crimes but the precedent it sets allows self identification as a way of committing crimes...
What I did notice was your last sentence
"to attempt to erode the societal standing of a group of people that actually exist and are already marginalised"
Which struck me as true about biological females as a group, not just Trans-women.