It's interesting that the fatphobia/HAES thing is brought up in relation to this.
I've been on the internet (and fat!) since I was a teenager in the mid-90s and have seen this movement go the same way as the trans crowd.
Back then fat acceptance started as something completely different to what it is now. Originally it was just to say 'we're here, we're fat, we're normal people, don't abuse us' type thing, ie fat acceptance of other people without abuse. Health At Every Size actually started by saying, 'yes, we're fat but that doesn't mean we can't exercise and do healthier things, do what you can and make a start on getting healthier'. Nothing like what it is now.
Then the usual militant lot start getting involved, purity spirals and identity politics ahoy, and it ends up being what it is now. As I've just said on another thread, most of this stems from American culture, you sort of have to pick a group and follow everything to its furthest possible end. Not just agree with what you want and leave the rest.
There's a lot of overlap with the self-diagnosed mental illness fanatics, self-diagnosed autistic people, the polyamorous crowd, the kink crowd, you'll even find it on pet-owning groups, hobby groups, etc.
It all follows the same pattern. It starts as a simple group for people with like-minded interests and it gets taken over by power-hungry people that change the direction into something completely different and other people get carried along with it.
Sorry for the long, offtopic post, it's been interesting to me for a while and I can see how this all started back before the internet was popular.