Well the core medical definition of ANY mental illness is caring about something way too much.
gender dysphoria is illogical condition because sane normal person should not care about gender at all. If you are a guy and you are getting hurt if someone misgenders you that's no different than being tranny who is being hurt by being misgendered.
Caring about opinions of other people also is sort of from of illness. And the most mentally healthy person by that definition will be psychopath who deos not care about anything at all.
So yes, you can manipulate another person into something by using their mental issues. But that person already has to be vulnerable with high level of neuroticism.