"But what prevents such Associations (the genderists' swim club, the genderists' lady club, etc etc) from being created?"
I don't mean to derail this thread in any way, but that is what the WI actually argued - that they were "the genderists' lady club".
The WI claimed that they did not rely on the single-sex exemption in the Equality Act at all but that they were open to anybody who was, subjectively, "living as a woman" and that this was a neutral policy and that they were treating men and women equally by only accepting those who were "living as women".
There are arguments against that.
Two of the cases mentioned in the TT transcript of the judicial review application were Al-Hijrah and Coll (Chief Inspector of Education v Al-Hijrah School [2017] EWCA Civ 1426, [2018] 1 WLR 1471 and R(Coll) v Secretary of State for Justice [2017] UKSC 40, [2017] 1 WLR 2093)
These two cases are authority for neutral rules do not preclude their treating one sex less favourably than the other and that will be direct discrimination. What looks like identical treatment does in fact constitute less favourable treatment on grounds of sex where such treatment causes a detriment for the complainant but would not do so for a comparator of the opposite sex.
If you have an association with a "genderist" criterion of "lives as a woman" then this allows women to live conventionally for their sex. Generally speaking, this is not going to be a burden for women since all that they are required to do is to carry on living as they always have done within the very broad parameters of whatever “live as women” means. Women are not required to alter how they live their lives in any way.
In contrast, a requirement that men must “live as women” involves a much greater burden. It involves utterly rejecting a conventional lifestyle, it may also involve the use of drugs and/or surgery.
A man is required to live a life outside of any sort of meaningful, conventional understanding of what being a man is. Women just have to go on living as they always have done. Framed like this, the "genderist" criterion is not neutral as between the sexes and is direct discrimination following Al-Hijrah and Coll.
And, of course, the opposite applies if the criterion is "lives as a man".
There was a discrimination case from back in 1996 (Smith v Safeway Plc [1996] EWCA Civ J0216-2, [1996] IRLR 456) which held that separate appearance and dress codes for men and women did not constitute sex discrimination on the ground that it represented a requirement of conventional appearance. The judge in the case said at one point:
“As [counsel for the employers] has pointed out, a code which made identical provisions for men and women but which resulted in one or other having an unconventional appearance, would have an unfavourable impact on that sex being compelled to appear in an unconventional mode. Can there be any doubt that a code which required all employees to have 18-inch hair, earrings and lipstick, would treat men unfavourably by requiring them to adopt an appearance at odds with conventional standards?”
I am not, in any way, equating "living as a woman" with wearing lipstick
In the above example, the treatment complained of is not merely a requirement to wear lipstick, it is a requirement for male employees to dress unconventionally for their sex while female employees are permitted to dress conventionally for their sex.
Requiring men to "live" unconventionally, but not women, is direct discrimination (arguably).
There is also a complicated argument about why this can be distinguished from indirect discrimination.
The above arguments would also apply, I believe, in the ponds case.
With the WI, there was also the fact that their constitution specifically referenced "women" so they couldn't include men or exclude trans-identifying women.