I don't support the premise of the statement, the quasi-religious belief that the liberal social system is a matrix of interlocking oppressions created by "cis white men" to maintain their privilege. Therefore, I don't believe that we need to dismantle our social structure to improve the lives of vulnerable people. The liberal social system, despite its flaws, has led to some of the most peaceful, equal, and prosperous societies in history. The new religion is anti-liberal and seeks to dismantle liberalism, even though many who have imbibed this ideology have zero understanding of liberalism and the role it has played in their own cushy lives. Before "dismantling" any structure or institution, one needs to know why it's there to begin with.
Smith's view is not "political correctness," it's "woke." And to the people who will dismiss the descriptor "woke" as a right-wing epithet: the term had a positive connotation among those who subscribe to the new religion as recently as 5 years ago. It denotes that a person has "awoken" to the real nature of society: that we're living in a matrix of oppression, and we must spend our lives "doing the work" to dismantle that system. The ideological, religious nature of this system is evident in the thought-terminating cliches that otherwise smart people use in place of logical argumentation: "trans women are women." This is a meaningless, circular statement that evades actual analysis. Sidestepping analysis is important when the argument relies on a hermetically sealed body of special texts instead of logic and rationality.
The misogyny in your argument stems from the way that you use women to prop up your argument while ignoring the concerns of women who keep telling you that they're worried about sexual violence. Every time a woman here points out the potential for danger or cites actual instances of violence, you call them hateful transphobes. Now, I'm not a standpoint epistemologist who thinks that women or any other vulnerable group has special godlike access to the truth, but in this case, the concerned women have lots and lots of data to support their claims about the potential danger posed by men. These data keep getting ignored or swept under the rug. Unless one believes in transubstantiation vis-a-vis gender identity (incredibly, many people seem to believe that the high preistess of gender ideology embedded in the soul of every trans-identifying person can proclaim a person the other sex and magically make it such), there is no credible reason to believe that trans-identifying males are safer than other males. More to the point: many people simply don't feel comfortable sharing changing rooms, locker rooms, etc. with the other sex. One person's comfort does not justify railroading another's discomfort.
I don't have a problem with gender neutral bathrooms and never said that I did. However, I do think it would be a mistake to convert all bathrooms and locker rooms into gender neutral places. Young people, especially women, are increasingly alienated from their own bodies and knowledge about the typical range of female bodies. Many have seen lots of highly-edited porn with breast implants and surgically-altered labia, bleached genitalia, etc. Some don't understand that their own bodies are normal. Sex-segregated spaces normalize non-sexual nudity and allow young people to experience unmediated reality. This is especially important as young people spend most of their time in disembodied interactions online.
Cue the gay jokes, but many of the men I know who played on sports teams developed comaraderie in the locker room. As I said, it's a place of non-sexual interaction--I'd even call it non-sexual intimacy.
As much as I admire Kipchoge's stoicism, human beings are limited. The nature of those limits is unclear, but history has taught us that unmitigated belief in the pliability of human beings and society is just as dangerous as using biology to justify existing social structures (probably worse in the short term). Hitler, Lenin, Stalin, Mao, and Pol Pot all thought they could remake human beings and society, and they killed millions of people just in the past ~150 years. There's a world of difference between acknowledging the ability of humans to reshape their existence and believing that all efforts to change people and society are inherently good and apt to be successful.
People are fallible, and I will not walk lockstep with arrogant fools who have annointed themselves as moral superiors armed with the exact directions to utopia. 2+2 = 5, trans women are women. This is the path to hell paved by ignorant, sanctimonious idealogues.
I don't buy this nonsense because its authoritarian. I'm a liberal who deeply values freedom of thought and expression. Acknowledging the fallibility of human beings is fundamental to a liberal society; this means rejecting any claims to special knowledge or authority that cannot be precisely articulated with reason and evidence.
This is the crux of the culture wars, BTW. It's not whether one is politically left or right, Democrat or Republican (in the US context). The greatest division right now is between liberals and anti-liberals. The latter group includes the religious right and practitioners of the new religion; these are mirror-image authoritarians.