Sorry to quote you twice, I wanted to make a second, separate, point.
"...whereas they do have a choice about whether they join the WI"
Have you never considered that perhaps there might be some reason why women might want a female only space?
How about self determination? That is, the power to make decisions for yourself.
The role of women in society has, historically, been disproportionately determined by others, that is, men. For this reason it is particularly important that women, without men - the ‘others’ who did all the previous determining - are able to decide matters of importance themselves.
Women need spaces of their own in order to self-determine, but also, by the act of creating spaces in which to be inaccessible, women are also exercising self-determination.
Self determination particularly justifies exclusion in spaces where there is the chance for women to talk and raise consciousness. This allows women to talk openly about and debate issues of interest from a female view without the presence of men (rather like here on MN).
Indeed, it has been part of the WI’s constitution since at least 1948 to
“[p]rovide for the fuller education of countrywomen in citizenship, in public questions both national and international, …”
The latest constitution puts it this way: “to advance the education of women and girls for the public benefit in all areas including (without limitation):
(i) local, national and international issues of political and social importance;”
.
Women also have an interest in respite from men; a break from male attitudes, expectations and behaviours. Women and men are generally socialised very differently, and this leads to differences in the average behaviour of women and men, which colours their interactions. Women are required to deal with these male attitudes, expectations and behaviours in mixed-sex spaces. Women-only spaces can provide an important respite from this.
There is no reason to think that transitioning (which does not necessarily involve hormones or surgery) would switch someone from demonstrating male-typical behaviour patterns to female-typical patterns. If trans-identifying men will bring some or all of these male-typical attitudes, expectations and behaviours into these spaces then that is, on its face, reason to exclude trans-identifying men from those spaces.
This rationale does not depend on it being the case that a particular male person would in fact bring male-socialised behaviours into a space. It is enough that women have to manage this possibility when men are around. Women-only spaces provide respite not just from certain sorts of behaviours, but from having to make contingency plans about what to do in light of certain sorts of behaviours - from being on guard.
.
Finally, it’s relevant that women established the WI themselves. Women funded, volunteered at, and ran the WI as services by women for women for the last 110 years. If other groups may benefit from access to such spaces it does not give them the automatic right to be included; such groups should do the same work that the women of the WI have done for the last 110 years and establish such spaces for themselves.
.
Also, don't forget that the WI is a single-sex charity and they would need to change their constitution to allow men to join. But they couldn't just limit it to trans-identifying men, they would have to include all men.
It is perhaps illustrative of how any suggestion of such a change might go down with members that they didn't even think of going with that option but simply gave up on the idea of becoming a mixed-sex association.