"Likewise does she, or does she not, fundamentally have the right to refuse to go to a person's house or allow them into her home to provide a service, because of their bio sex, if they "identify" as a woman?"
The Member had different reasons for dismissing each of JY's complaints. In one the waxer did not have any issue accepting JY's appointment even after the 'reveal' that they were transgender, but eventually cancelled on the basis that "she found Ms. Yaniv’s behaviour troubling and deceptive – which it was."
So it avoids that question - as does a lot of the judgement. As you say, it is convenient for the member that JY provided so many reasons for the case to be dismissed.
If you provided arm/leg waxing you might reasonably expect a proportion of your clients to be male (not necessarily transgender) so you would probably have your own policies about who you do/do not allow to come into your home which I guess would have to be non-discriminatory re protected characteristics.