Back in the 00s, the anti-LGBT culture war targeted primarily gay people, and it primarily used religious arguments. The Bible condemns homosexuality, marriage is a sacred institution, it's a violation of Christians' rights to make their churches marry gay people, &c.
Clearly, it didn't work. During the 10s, when gay marriage was legalized, conservatives were dealt a pretty decisive blow on their anti-gay agenda, and so they shifted from targeting the LGB to targeting the T (they always targeted trans people, of course, but they really ramped it up during the 10s). With this change in focus came a shift in rhetoric. The right-wing certainly does argue for oppressing trans people on religious grounds, but you're a lot more likely to hear them use scientific-sounding justifications. They'll talk about chromosomes, about anatomy, about how "biologically there are only two genders," about "people trying to put their feelings above objective reality." They'll throw around words like "rational" and "reason." This of course ignores all kinds of actual science, such as the degree to which gender is culturally constructed, the existence of intersex people, how gender affirming care is the only dysphoria treatment shown to be effective, and a thousand other things. It's anti-scientific to its core, but it can fool a casual observer into thinking it's scientific if it's telling them what they want to hear. It's a bigotry for a materialist age, palatable to bazinga brains and nu-atheist Redditors, and maybe it's just anecdotal, but it seems to me to have more traction among a younger, hipper crowd than the religious arguments ever did.
I can't help but wonder if this pivot was concocted in some right-wing think tank somewhere.
They're not edge or corner cases. What we consider male and female is socially constructed around presumed reproductive roles. This is the biological component. Every human society in existence would presume my sex is female because I am phenotypically female. Only a geneticist would add the caveat that I'm karyotypically male (if I even am - who the fuck knows cause even in the 21st century we don't do chromosome testing at birth). Let me also remind you that the gender/sex distinction is historically new! Most human societies would agree that I have changed my sex. It's only in the 20th and 21st century that people would dispute that, because the idea that sociological sex and biological sexes (whether it's genetic or reproductice or something else) are the same has become widely accepted. Speaking of birth sexing, sexes are socially assigned at birth according to genitals. This is why intersex babies get "corrected." Yet not all intersex conditions are obvious by looking at genitals. What would you call a condition that causes "females" to have "male" secondary sex characteristics? That's an intersex condition. Yet PCOS does this in up to a fifth of some female populations yet society does not consider it an intersex condition. Because patriarchal society insists upon the sorting of everyone into a sex binary (an immutable one at that, nowadays - a clear reaction against transhood) despite it clearly being bimodal and malleable. The body is artificially sexed. Women are not naturally hairless, yet body hair is considered male. The everyday Mesoamerican woman was as ripped as a professional kayaker from all the corn grinding she did, but the female sex is seen as dainty. The anti-trans movement wants to ban trans women from chess, darts, and Jeopardy! What is this if not 19th century sex science claiming women have inferior intelligence and motor skills?! Finally, let me remind you that humans are capable of generalized labor, and are thus able to change their environment. As a result, we have created exogenous hormones and sex reassignment surgeries. Trans people could change their sociological sex centuries ago. Now they can change their phenotypical sex. It is only a matter of time before we start growing reproductive organs from our own cells and having them surgically implanted. Nature is unjust, but we can change our nature!
Trans people are edge and corner cases when it comes to current popular definitions of gender. For 99% of people there is no difference between their sex and gender which is my point. Most rationalist transphobia comes from people not looking at edge cases because a traditional definition of sex such as which gametes does someone produce or what genitals they have work for 99% people. With the chess case it's a little more complicated than that because women's cheese leauges started as a means to provide women a space with a smaller competitive pool and fast-track women to the upper echelons of the sport and then believing trans women threatened that pipeline; it didn't necessarily come from a belief that women were inferior and women's chess leagues were seen as a means to make the sport more popular to girls, like what motorsports are doing today. And yes, gender is a means of oppression and weaponized impractically.