Actually, I think RW Christians in the US - evangelical and other types - are more divided on this topic than you say. Whilst some are jumping on the child trans bandwagon because they're homophobes who'd rather have a trans kid than a gay one, others are very much against transing, especially of kids.

Moreover, many on the secular right in the US - be they moderate Republicans or more extreme, hard-right factions - have spoken out against the trans craze because they think it's harmful both to children and an affront to girls and women's rights. The only mainstream media outlets that are allowing genderist critical views - including radical feminist ones - to get any public airing are conservative ones like The National Review, The Federalist, The NY Post and Fox News.

At the same time, though, many prominent TIMs in the USA pushing transgenderism such as Jenner, Pritzker, Tur, Kristen Beck are right wing men who are highly militaristic too. And as Amy Bloom documented in The Atlantic in 2002, the TIM movement is one of "Conservative Men in Conservative Dresses."*

In the Democratic Party, it's both woke "left" figures like AOC and Elizabeth Warren as well as the longstanding establishment honchos like Biden, Pelosi and Nadler that are pushing transgenderism and calling for gender to replace and supplant sex in anti-discrimination law. Bernie seemed to have tried to resist throwing in his support for quite a while, but now it seems he's jumped - or been forced to jump - on the bandwagon too.

*I tried to post a link to the Bloom article. In response to complaints and harassment by the same TIMs who've gone after J Michael Bailey and other sexologists, The Atlantic scrubbed it from its site years ago, but it used to be available elsewhere online. But now it seems have been scrubbed from those other sites and pages too. I think the gist of it is contained in her book 2003 "Normal."