As for feminism causing transgenderism, it seems not. I don't think there's been a definitive study, but anecdotally it seems gender troubled kids are more likely to come from very conservative families, often religious, where gender roles are rigid and the parents would rather have a transgirl than a gay son.
Feminists don't like gender at all, so are far less likely to interpret gender variant behaviour as meaning a child is transgender or to encourage them to become lifelong medical patients or undergo surgery on healthy tissue.