I am not pretending your posts don't exist. I cannot answer every single post on this subject. However, my answer to you is much the same as to others.
If the WI continue to admit trans women, they are not covered by the exemption in Schedule 16. That does not automatically mean that excluding some men is unlawful.
It is unlawful if they are being excluded simply because they are men, which is clearly not the case. It is potentially unlawful if they are being excluded because they don't have a characteristic which is shared by most women but few men (indirect discrimination), but even then it is not unlawful if it is a proportionate means to achieving a legitimate aim.
Putting aside arguments as to whether the WI's approach is indirect discrimination (which is unclear) and assuming that it is, we know from case law that the courts give membership associations like the WI a lot more latitude than employers, public bodies, etc. I doubt there are huge numbers of men wanting to join the WI who are being prevented from doing so by the current rules. The bar for having a legitimate aim is therefore likely to be very low. Something as simple as wanting to be inclusive of all womanhood could be enough.
We don't know for sure. The only way to know for sure is if someone takes the WI to court. If they did, my view is that the WI would win, but I wouldn't bet the house on it.
Edited to add...
As for "no men" statements and similar, it depends on context. The Supreme Court decision does not mean that "no men" has to mean "no biological men".