I always thought that "case-by-case" was for the situation not the individual. (although often misinterpreted due to poor drafting of the EA).
e.g. A women's rape survivors group. This is an excellent case for a female only service, with no males allowed in (however they identify).
Not, we'll let one transwoman in to this group, but not hypothetical Pete who also identifies as as a women. The case for this group is that all males, assigned male at birth, transwomen, male non-binary (etc.) are not permitted.
So in this case the NHS should have decided on the case for the female changing rooms. Are men (however they identify) permitted in or not? Rather than saying it's ok for one male who says they are a transwoman but would deny a different male who says they are transwoman.