I think you misunderstand me, or maybe I wasn't very clear.
Everything you highlighted is worth highlighting, and I think if the gender critical movement focused its energies on the injustices you mention, more people would engage.
But because the noisiest, less thoughtful, elements of the movement are breathlessly sharing clickbait from the Telegraph on vegan tampons in men's loos, individual DL chestfeeding leaflets from one service provider within one NHS trust, and misleadingly framed images of toilet signage to make it look like there's less single sex provision for women, the whole movement gets tarnished with a sense of... ridiculous hyperbole.
Because many people are bright enough to know that one toilet in one National Trust property does not a policy make, nor does a single DL leaflet in the vast sea of NHS leaflets mean women are being eradicated from public life... Most people don't give a shit if there are tampons in men's loos, or even guidance on chestfeeding, because they can see that, holistically, 99.99% of men's loos don't have tampons in, and 99.99% of breastfeeding literature mentions women and breasts.
Gender critical is starting to become synonymous with reactionary hyperbole. I would have described myself as gender critical ten years ago - now I wouldn't, because it's all got very... hyperbolic, is the only word I can use. Can't see the wood for the trees. Indiscriminately angry about and reacting to everything, rather than focused anger on big issues. I only say this in response to the question, 'Is it the phrase gender critical that makes people unwilling to engage?'. No, because 'Sex affirming' would still come with the same hyperbolic, seemingly actively seeking to be offended, drama.