This is a battle with different fronts. For legislature, we stick to facts and material reality because that is the essence of we need in law to protect.
For making the case with those taken in by the effective PR from the genderists, we need to counter the emotional fluff with factual reality, yes, but also pierce through all those assumptions and the conditioning of genderist thinking which has been prevalent for way more generations than just the last 50 years. Remember, the trans stuff is just the modern iteration of every sex stereotype in the system that feminists have been pushing back against since the year dot.
Gina Martin thinks she has already struck the patriarchy hard, and sees herself as part of the modern feminists whose mission is to right the wrongs of the entire human race. If you're a victim, anywhere, of anything, feminism is for you. That's a big play in the PopFem crowd, and it's all emotion based.
You don't pop that bubble with stats and logic, sadly. You do it by demonstrating that PopFem betrays the women it thinks it is for. You show the PopFeminist that she's dismissing the very women she is purporting to stand for. You make her notice her hypocrisy and then you give her the space to move away from it.
Now, I'm not saying everyone has to do this, or even do it all the time. Some of us do the first bit well, others do the second. That's ok. But both are necessary, and the Gina Martin's of the world will need to be countered with both approaches.