Getting this into men's awareness could make a real difference. The best way to do this is concrete examples, e.g. children (blockers and cross-sex hormones) and vulnerable women (medical treatment like above, male rapists in women's prisons) being put at risk, men cheating in women's sports, lesbians being put under pressure to have sex with men, etc.
The way to get the glazed over response is to go into the theory and to use the jargon. "There was a 60 year old woman in Hyde Park meeting other women to discuss bad changes to the law who was battered by a man pretending to be a woman" is more effective than endless TERF, M2T, TIM, "cis", non-binary.