It's mainstream in the US. Far right is not an accurate descriptor, they are more like neoconservative.
en.wikipedia.org/wiki/The_Heritage_Foundation
As you correctly identify, the American College of Pediatricians is a small (500 members, cf. the American Academy of Pediatrics with 64,000) group of conservative doctors.
The question is WHERE is the impetus for this comes from. Hoping that Prof. Winston will campaign on this issue is wishful thinking IMO.
The parties:
(a) TERFs ('old white women')
(b) social conservatives
(c) a tiny handful of people, e.g., gender critical parents with trans children
verus:
(a) Angry violent men (trans) with the law and on their side
(b) Socially conditioned liberals who have been told that the angry men are victims
(c) The entire medical establishment
(d) The entire political establishment in Western Europe
(e) The entire educational establishment
I don't see how this ends up with anything other than the angry violent men getting what they want.
And as you identify, having the same arguments as the anti-abortionist, anti-gay marriage, anti-sex-before-marriage, US conservatives, is likely to lose you support.
I'm not sure exactly if history is a cycle of liberalism followed by increasing conservatism, but my sense is that in the UK the current trans rights movement is perceived is all part of the same wave of progress as banning racism, homophobia, and that it's not seen as a cycle but rather an ongoing process of improvement, ever increasing tolerance.
I think this is a misguided view of history - in the 70s, paedophile rights were a popular cause of the left, in the early part of the 20th century eugenics was seen as all part of the wave of human progress. So it now seems that the TRAs will inevitably get everything they want and perhaps in due course and half-a-century down the road we will go through a similar process of reappraisal that we did with lobotomy, eugenics, and other past errors.
But for the time being, as I think you allude to, we are on the wrong side of history - the social conservatives are by definition opposed to progress and this is progress and if you don't agree well you are isolated I am afraid.