Honestly, from a design perspective I do think the one on the right is actually better in some respects. Yes, it wouldn't scale well, there's too many colours, it's too busy, but it has some good points. The font choice draws you in more, with less space between the letters making it easier to read at a glance and the 'f' creating interest. And the house is actually united with the text, whereas in the left image it feels completely disconnected.
I would be pretty disappointed if I'd paid for a logo and I got the left image tbh, it's not very interesting or memorable. Yes, fuck AI, but I'm not sure this is the best comparison because both logos suck in different ways.
The experiences trans men and women have with misogyny will never not be fascinating to me. Like, for the first time ever we have this huge sample size of people who have experienced how their gender presentation affects how people interact with them, giving tangible proof of misogyny in action. And it can't just be swept aside with 'MaYbE tHe wOmEn JuSt miSuNDerStOoD' or 'mAYbe tHe mAN diDN't MeAn iT LiKE tHaT'. I mean idiots will still make idiot arguments but at least it chips away at them a little bit.