The vast majority of assaults commited in these spaces have absolutely nothing to do with a trans person or a person claiming to be trans. The people behind that claim have since admitted it was a lie to try and undermine trans rights.
If you want to be very strict on segregation by sex, surely you must have a method to ensure that all service providers can do so.
And no, time and again you’ve proven that you cannot always tell, so please don’t use a subjective measure.