If only real life were as simple. But since you claim that you originally posted the image in order to spark a discussion on the linguistics of the word "woman", then I think you know that the question here - with both A) and B) - is what the definition of "females" and "males" actually is.
There seems to be a suggestion that it's necessarily linked to the physical, but there are a number of academic papers and references which maintain that social dysphoria can be had without body dysphoria, and that both are gender dysphoria. There seems to be an even stronger suggestion that social dysphoria either isn't real and people are just pretending, or that it doesn't matter. But I've seen research which suggests that of the two it's social dysphoria that causes by far the most amount of distress to transgender and non-binary people. And I think that declaring the field of psychology to be wrong on any particular issue really requires more than incredulity or ridicule.
So what are the various viewpoints, and how is it possible to reach a solution that caters to everybody's needs? I don't know. I do know it's not as simple as you're presenting it to be.
Even you know it's not as simple as you're presenting it to be, at least if you read your own link. The whole thing apparently started because the individual in question was welcomed into a women's only group and one member wasn't happy about it. It seems that the other members were. So what does that mean for "leav[ing] it up to the women for whom the spaces were originally set aside" (assuming by that that you mean cis women)? How many women have to object for it to become not okay? How do you avoid the tyranny of the majority whichever way the chips fall?