Parents would not consent but for the child saying they are ‘meant to be the opposite sex’. So in effect, it is the child consenting.
Some parents will be convinced by their child telling them that they need blockers. Some will be terrified, because of the suicide narrative that has been deliberately and recklessly pushed, over and over, that if they don't do as instructed, they may lose their child, either to estrangement or suicide.
Some parents may have other reasons for wanting to stop the development of their child, and/or wanting a child of the different sex.
In most cases, parents only want the best for their child, of course. But we also cannot ignore the existence of abusive parents. It should also be noted that the statistic about parents and convictions for sexual abuse, from the GIDS patients.
There are also some parents with strong beliefs about, for example, reincarnation, who have 'trans' children, who I would say are unbalanced themselves. Munchhausens by proxy is a thing.