I can't see how this can possibly work. Conversion therapy for homosexuality / bisexuality can be defined because homosexuality can be defined.
However, afaik it isn't conversion therapy to try and stop a vegan being a vegan, or a Catholic a Catholic. I don't think conversion therapy applies to beliefs (?)
Obviously children being transed by homophobic parents will be impacted by this, but I don't see how (or even if it should) impact children who identify as trans.
Medical transition should be prevented by strict guidelines (which I'd hope already exist) on giving physically healthy children unproven and experimental treatments with known extremely adverse side effects.
Social transition should be stopped by schools and social workers as it is very unlikely to be in the best interests of the children in the long run.
Mermaids et al should be stopped because they are pushing both medical and social transition, for the reasons above.
In most cases I'm not sure that conversion therapy is actually relevant? The problem is that everyone (Inc the government) is treating gender identity as if it is a tangible thing that can be positively identified as opposed to a nebulous internally inconsistent belief system.