@Ides
I think that this issue is one of those that shows that we've come to the 'end of feminism', in a crucial sense. The whole thrust of feminism, for over a century, has been that women could do what men do. That's been entirely correct, in my view: the strength of humans, relative to other species, is all about humans' mental capacities. Never about their physical capacities. Relative to chimps, horses or even tigers, the difference between men and women is
tiny.
Humans' strength is in their brains. And there's sod all difference between men and women in that respect - if any at all.
The GC argument is anti-feminist. It wants to assert that women are inherently inferior to men in ways that are still in some way important. It also wants to assert that women are, in various ways, nicer than men, in some crucial respects. This is why GC advocates are fine with any kind of natal woman in a woman's bathroom - because women are unfailingly lovely and fluffy - whereas any self-identifying woman, no matter how small and fragile she is - if she has a penis and testicles, or even once had a penis and testicles, is, ipso facto, a menace to all the women around her.
Sport is sport. Whatever. A tiny percentage of women will ever be involved in it to any great standard. The tiniest of tiniest percentages of transwomen will ever be involved in it at that level ... the fingers of one hand, maybe.
Gah ... of all the things we women have to face, the issue of transwomen is so, so tiny. I really do think we should move on from it. It makes us look silly, tiny and weak that we're so scared of people who were born equipped with penises and testicles. We are better than this ridiculous argument.
Others have responded to the top three paragraphs in Ides' quote so I want to address the fourth one:
This issue is, unfortunately, not tiny, because it is really not only an issue about trans women:
The new gender ideology aims at erasing our ability to define ourselves as biologically female (because it says that we cannot call ourselves women on the basis of biology), it erases our ability to unite politically to further our shared interests (reproductive rights, safety from sexual violence etc.), and it ultimately would erase our ability to continue the kind of work previous generations of feminists began.
Consider how the globally oppressed sex class 'women' compares to the new identity sub-category 'cisgender women.' The former definition draws our attention to a giant group which is often mistreated. The latter definition (containing the vast majority of the women in the former) suggests that this group is now privileged and favoured.
Consider how the female body is turned into a gender-neutral one: It is now 'bleeders' who have periods, and 'people' who get pregnant and give birth.
In the most extreme form of the gender ideology, there is no female sex, though there still is a male sex which can be called 'men'. The female sex is nameless, even though it is oppression on the basis of that sex which remains a big problem on the global level.
Consider how transitioning from 'women' to 'nonbinary' really means that the person is "not like those other girls" who are expected to be content with regressive female sex norms, but instead is an actual individual human being who should not be treated with sexist expectations and so on. (That is, of course, what feminists fought for, only for all women, not just for a handful.)
Yet many individuals matching that nonbinary description sometimes want to be 'included' in their old group. This is because they, too, may need abortions or defense from sex-based discrimination. But this 'inclusion' requires that the female body must be made gender-neutral. This turns the female body into a gender-neutral 'people-body' which apparently any random person can suddenly possess. It also erases the gender definitions of all women who base them on the sex of their bodies.
Once we get to this point, the meaning of the term 'women' becomes opaque. The alternative definitions I have seen are all deeply sexist or circular or empirically empty. This matters if we wish to fight against sex-based mistreatment, as it turns the group suffering from it into just 'people' and makes it pretty hard to see what something like 'women's rights' might even mean.
So this is not a tiny issue at all. In some ways it is a fundamental challenge to feminism and some parts of it are, in fact, closer to traditional anti-feminist arguments than feminism:
The posthumous transing of many famous female role models from history suggests that no mere woman could have done anything so courageous or important, the assumption that a boy wanting to wear dresses must really be a girl because it is girls who wear dresses, not boys, suggests a direct link between gender ideology beliefs and traditional sex norms and so on.