Archery is spot on in her analysis. It's about how it plays to the wider audience.
It makes me think of Clinton's "basket of deplorables" comment. In context (and I saw the whole clip at the time) she was trying to talk about a small subset of people, not the whole of the Trump voter base. But as soon as I heard it I just had my head in my hands - because whatever she was trying to say was not what people would actually hear - I remember turning to my friend who was watching TV with me and saying "did she learn nothing from watching the Brexit campaign unfold?"
Yes, we need to talk about AGP. Yes, we have to expose it to the light of day. But we need to be careful how we do it. Saying "Stonewall have messed up by lumping together genuine transsexuals who suffer from extreme discomfort about their sexed bodies with a group of people who aren't really trans at all, but have a sexual fetish for cross dressing" gets the point across. Using dog-whistle words like "parasite" (yes, I know that the word actually used was "parasitic", but no-one is going to remember that 6 months from now, I can guarantee it) means people leap to conclusions about your motives and completely misunderstand and misrepresent what you're trying to say, and switch off from listening to you.
The other advice I'd give is "describe what people do, but don't try to ascribe motives to them." Showing photos of the body suits gets the point across perfectly - incontestable facts. Most people will recoil from this. Start to impute motives ("they're doing this because they're perverts who want to co-opt womanhood"), and you allow the whole discussion to be derailed into a "perhaps that's not why they're actually doing it, AGP isn't a thing" side-road.
Simply saying "I don't want to be naked in a changing room with people who behave like this" is a much more powerful message.
(In a way it reminds me of the arguments about DV - someone will come on here, and because they've had years of being gaslit, they will think the important thing is to get to the bottom of why their partner is behaving this way. What they actually need is a reality check which says "the why is irrelevant, all that matters is that he is doing it - behaving like that is unacceptable and you need out of that relationship.)