It is clear from the SC ruling that any exclusion of a trans person from single sex services has to be a proportionate means of achieving a legitimate aim.
Sleight of hand. Only someone who understands the law could have crafted this true, yet totally misleading, statement, and it does not reflect well on their honesty.
For the benefit of anyone who was confused:
It is never illegal discrimination to exclude, from a single-sex space, a member of the opposite sex, even if they identity as the sex the space is intended for.
It is sometimes illegal discrimination to exclude, from a single-sex space, a member of the sex the space is intended for, if it is on account of another protected characteristic.
If that characteristic is gender reassignment, the exclusion must be a proportionate means of achieving a legitimate aim, to be permitted.
For example, a woman's efforts to disguise herself as a man may be so successful that her presence would cause alarm.
(Women who do not identify as men, but who appear male for some other reason, can also legally be excluded, as a Schedule 3 derogation from the general ban on perceptive sex discrimination. Unlike for transmen, the guidance does not urge alternative unisex provision for them. Their legal position was unchanged by FWS so I guess they're used to it by now.)