I'm afraid those of us looking on aghast just don't understand how powerful the concept of the trans child is. It's absolutely bamboozled so many previously sane and skeptical people. Scientists and doctors have put aside their normal mindset to fully get on board, because to deny the child is the biggest sin of all.
I also think that people have looked at previous social justice movements (for women, ironically, and blacks, gays, disabled) and want to be fully on board and fully able to signal solidarity in social situations.
Throw in humans' need to belong to groups, atomisation of society to pure binaries (if you don't agree with me, you're against me), and the vast majority of these people having a trans child and/or knowing people with one, and not having their rights personally downgraded or threatened as so many women have, and you have the basis of where we are.
And if any doctors or scientists are doubting themselves, the sunk costs that are so deeply buried are too painful to reconcile and cash in, it's so much easier to keep playing the same record over and over.
This is my take as to how Dara O'Briain, Dr. Brian Cox, the Van Tulleken TV doctor twins, Sir Richard Attenborough, and every scientist and doctor that tacitly doesn't kick back against this trend, is reconciling their position in supporting pseudo science less reputable than astrology, crystal healing, homeopathy, psychic phenomena and ghost hunting etc.