The issue to me is that the mother, who used to be a mental health nurse, has been so indoctrinated into the cause of transgenderism that she has got to the stage where she sees it everywhere, even where it isn't. Gender dysphoria exists, but it's extremely rare and it's certainly hard to see how a four year old can even understand the very concept.
This is the real issue with these whacky theories - the people who believe in them hold them as a matter of faith. In most cases they are a substitute for faith. Worse, they impose them on other people, usually very vulnerable people like their infant children. This kid is going to be mentally scarred by all this for years, maybe for life.