"I have no idea why people who are anti-trans are also pushing 'gender norms' when this seems like it would have the exact opposite effect?"
Do you have groups mixed up?
What feminists who believe that no person can change sex are 'pushing gender norms'? The feminists that I read responses from are saying 'there are no right ways for female people to be girls or women except to have a female body'. They will be the people saying 'if you are a little boy who loves shoes (or hobbies, clothes, music, toiletries, colours, TV shows, hairstyles, artists etc etc), go for it! It doesn't make you a girl though!'.
However, it is also true that 'boys needed to learn that some things were for girls'. When something is designated as being a single sex provision, such as Brownies / Guides and sports, then yes, boys need to learn that some things are for 'girls'.
I wasn't on the thread, but I would be surprised if any poster was posting from a feminist perspective and declaring that ballet flats were to be rejected because they were 'for girls only'. I wouldn't be surprised if they said that they were designed ergonomically for girl's feet and that there might be issues with fit. But that is not what you are saying they meant.
Whereas, there is a group of people who have even presented in UK schools that said that if you were a girl and loved football then you might be a boy and if you were a boy and you liked barbie, you might be a girl.
edit: Cross posted with Keating.