I think what this highlights, is that gender identity is not a true "identity" in the mathematical sense.
An identity works like this:
If A=B, then B=A (an vice-versa)
It can be something that makes an individual unique (your NHS number)
Or it can be a shared characteristic within a group of individuals ("all the people named Bob")
In either case, the identity relationship is reciprocal ("if my first name is the same as yours, then your first name is the same as mine")
That's how you can use it to define consistent sets of individuals based on "sameness". Sameness must be mutual, regardless of what criteria of sameness you pick.
The officer may or may not identify as female (unknowable)
But the bottom line here, is the protester does not identify him as female. She does not identify him, as being like her (part of the same class of individuals). This "gender identity" feeling is not just unknowable, it is also often not mutual.
In other words, "gender identity" is a logical fallacy.
(also, is this particular case... how would the "female-identifying" officer know if the protester identifies as a non-binary individual constantly oscillating between male and female, and therefore, unpattable? The legal ramifications of gender identity are endless...)