That episode of South Park where Richard Dawkins freaks out when he finds out his girlfriend Mrs. Garrison was trans, and unravels his budding atheist world empire because of this, was so prescient.
But here's my attempt at figuring out what happened. Those anti-evangelical British Lib Dem/Labour atheists (e.g., Richard Dawkins, Graham Linehan, Ayaan Hirsi Ali, Stephen Fry, Maajid Nawaz John Cleese, Ricky Gervais) who were so beloved by libs in the Bush and early Obama eras, splintered from the younger liberals/leftists on the degree to which the west should tolerate Muslims, and attributed this split to younger people's obsessions with "political correctness." They began bleeding their following, and got extremely obsessed with affecting a "nuanced intellectual" persona and reveling in their persecution complex by going "I'm as liberal as they come but the modern left is doing ____ too much and is even calling ME a racist and sexist!"
The alt-right/chuds/Conservative dark money network loved hearing this shit and started glomming onto these people, because their movement was dying and needed a less cringe, marginally more secular sheen. Suddenly these atheist personalities found that their cries about political correctness on videos/podcasts would always garner a huge response (even if it's from the right), and so started playing this shit up more. Around the same time JK Rowling was getting obsessed with twitter because she regularly dunked on Trump and got fawned over by Tumblr-types. However, as she reveled daily in adoration, once she did get criticisms about her trepidation towards trans people and Jeremy Corbyn, it was like turning off her pleasure tap, and drove her insane.
All this converged in the form of bitter Brit atheists backing JK Rowling because of their shared animosity toward the younger left's "coddling" and "cancel culture" (i.e. not thinking they were the ideological vanguard anymore). Once Caitlin Flanagan's article "The Coddling of the American Mind" framed this behavior of the younger left as an open academic inquiry issue, a new collective of influential "anti-PC" web personalities was born.
The Brit libs became willing to do anything to stick it to the young people who didn't like them anymore, and began jamming up liberal spaces with claims that reducing racist/transphobic literature from college syllabi was hindering "free inquiry" and "intellectual growth." This got them invites to Real Time with Bill Maher, JRE, and the Rubin Report, and even suckered many liberal/leftist comedians/academics like Whitney Cummings/Kumail Nanjiani/Zizek/Finkelstein. So they just stayed stuck like this and helped portray Rowling as a martyr, and "serious concerns" about the "excess" of trans rights became the mainstream UK culture among even the Labour Party, subsequently even echoed and appreciated by Hillary Clinton.
That's a great explanation that's much more big picture, as I recall some of the #FBPE libs were even blaming Brexit passing on the left being too PC and pro-trans, thereby aggravating the leavers too much.