Trick to sidestep equality law?

They asked and voted many years ago to remain single-sex.

‘gender’ is highly correlated with ‘sex’ - that is the whole reason why men want to access girl guides. You cannot discriminate on the basis of sex other than in accordance with the EA exemptions so discrimination on the basis of gender would be unlawful as it is unlawfully discriminating on the basis of sex.

The courts are quite clear on this concept - they have regularly ruled that certain things are discriminatory because they disproportionally impact one PC more.

@Gerri1992 no this wouldn't work because the people who drafted the original Equalities Act were not stupid and the legislation already covers such underhand attempts to subvert it.

In general, all people should be treated as equal. It is ok to provide services differently to people on the basis of protected characteristics where it is a reasonable means to achieve a legitimate aim (eg having social organisations for women and girls like the WI and girl guides is a recognised way to help women and girls to overcome and transcend the disadvantages faced by female people within a patriarchy and that is something that affects transmen because their sex is female,but doesnot affect transwomen because their sex is male and frankly the sense of entitlement with which the desires of tranwomen are promoted above the needs of women is very much in keeping with promoting the patriarchy) - if they are not doing that then they need to be open to everyone.

What they would be doing if they restrict access on the basis of "gender" ie allow entry to anyone with a feminine gender would come under the definition of "indirect discrimination" in the same way that banning people who are wearing headscarves from a premises would be indirect discrimination against muslim people even though not all muslim people wear headscarves and not all people wearing headscarves are muslim but because the restriction will disproportionately affect muslims more than non-muslims. In the same way, any restriction on the basis of gender would automatically always disproportionately affect one sex more than the other and therefore would automatically be indirect sex discrimination.

The scouts went mixed sex so Guides could do it but as others have said, the trans activists would then lose all interest in joining.

If you set identical entry requirements but very few of a particular protected characteristic would be able to meet those requirements it can be indirect discrimination.

It depends on what the entry requirements are set as.

How can this work when all humans would still be of one sex or the other and sex is a protected characteristic?
Magic wand to unsex everyone?

It wouldn't be discriminating against men unless they had different entry criteria for men than for women.

Just to add, though, that they couldn't, in their female-gender-based organisation, admit females just on the grounds of their sexed female bodies and have a different criterion for males -- eg that they liked dresses and pink and being called female. That would be sex discrimination.
The criteria for both sexes would have to be dresses/pink/princess/etc. I would not be eligible for a female-gendered-based organisation despite being a woman.

I think it would be indirect sex discrimination against men.

If only people of woman gender* can join then that would exclude most men as they as a sex class are less likely to have a woman gender than women as a sex class so the gender requirements are indirectly discrimating against men as a sex class

*assuming woman gender can be defined

Well, and they could, couldn't they? Provided they could work out a reliable definition of what it is to have a certain gender.

People are free to form associations on all sorts of bases. It wouldn't violate equality legislation. There is nothing wrong as such with having a mixed sex organisation. And there is nothing wrong with having an organisation that (I dunno exactly ...) only catered to people who liked pink and princesses or whatever the flip would be their basis for assigning gender.

If they had any actual fucking brains, they would ask their members if they wanted
Single Sex
Mixed sex with a rebrand to 'The Institute' or 'The Guides'

And see what their actual membership wants.

It's interesting reading posts like this one linked, because it's an admission that sex is indeed real and not at all the same as gender ID. Yet I'm guessing it is written by a Believer in gender ideology?

I think the club more analogous to having a chess or Tory club would be having a club for fans of gender ID. But I don't see how they could lawfully exclude males without special identities and females with special identities from the same club.

At which point of course the transgender “community” would lose all interest in joining them, since their only aim is to join (or more often IMO help to run) an all-female organisation.

It wouldn't work using the word 'gender', but all these places could become mixed sex.
The issue is basically that to stop the risk of discrimination claims, they have to accept all males, not just a subset of allegedly trans identified males.
But if they can change their Articles of Association or whatever their founding documentation is, they can just drop 'girl' or 'women' and accept both sexes.