Puberty blockers stop physiological changes to the body that do not fit a child’s gender identity, while the hormones go a step further and allow children to change physically and go through puberty with the gender they identify as.
I think this sentence sums up all that is wrong with this ideology.
What rational person would think it appropriate to stop physiological changes to a child's body that do not fit an 'identity' that they think they have at that time?
What rational adult believes that it's possible for a child to "go through puberty with the gender they identify as"? Nobody has ever changed sex by taking opposite sex hormones.