4thWaveNow, the website for parents and others concerned about the new affirmative approach to gender questioning/nonconforming children and teenagers, keeps an eye on various open Facebook groups where gender practitioners in the US and Canada discuss issues. The link here is to the first in a series of tweets with screenshots from a recent discussion following a query from a parent with a child on the autistic spectrum.
The child socially transitioned at 4 and is now 8. The mother explains My daughter has been dealing with her transition by disassociating herself from the person she was and has created an entirely new identity and birth year. She also has autism which compounds how she interprets reality and deals with life. My concern is for her happiness and well-being! The time for hormone blockers will be coming in the next few years and I worry because she refuses to accept the reality that she is transgender and is insistent that she was born a girl and my worry is that she may be denied blockers because she will not admit to having male body parts/puberty. She says she doesn’t need blockers because she “is NOT a boy and was born a girl so why would she need blockers?”
It's clear from what the mother says that the child was extremely unhappy at four and was fixated on having the wrong genitals, saying 'I want to die' 
. Of course the mother wanted her child to be happy and medical professionals have told her that affirmative treatment was the way to go. But a child on the autistic spectrum thinks very literally indeed and tends to be very rulebound, because, lacking the ability to intuit things, they look for rules to follow to navigate their way through life. Gender stereotypes are like rules. Children on the spectrum often find it extremely distressing not to be able to follow the rules.
Based on my own experience of raising a child on the spectrum, if that child had been mine I'd have wanted them to have therapy from someone with a really good understanding of autism as well as any co-morbid conditions like depression and anxiety, which are very common because these children find it so hard to fit in and make friends, and they get bullied so much. I'd also have wanted the professionals involved to take account of the fact that for children on the spectrum emotional maturity tends to lag well behind intellectual maturity. I don't feel that any pre-pubertal child has the maturity to know what they are giving up if they go on puberty blockers but children on the spectrum are surely the least capable of grasping this.
The discussion from the professionals, though, is largely about which drugs the child should have and when.
I don't think things would have panned out in quite the same way over here because the NHS does a lot of gatekeeping. Worrying, though. Parents with the funds to go privately and especially to go abroad could be doing this in the UK already.