Breast feeding facilities aren’t mother and baby rooms.
So who else other than women/mothers breastfeeds their kids? The straightforward, simple, only biologically-possible answer to that question is 'no one'. Non-binary people might not adhere to tired gender stereotypes, and that's commendable, but physically and anatomically they are still either male or female.
I have no skin in this game: I breastfed in public without a care. Not every woman feels they can or wants to. And that's fine. But as for women doubling down and being strident over these issues, fostering a closed-shop attitude to men in BF groups, etc and not wanting to welcome 'My Nigel', I think it's quite a safe assumption that many of us did not start out this way. Females are socialized to be polite to men, 'let him down gently', and always be kind. It can be hard to overcome conditioning which has been drummed into most of us since birth.
And that's precisely where this attitude has brought us. These responses have to be viewed in the context surrounding roughly the past seven years, which have seen a sustained assault on our rights, our spaces, and has even come to view 'woman' itself as a dirty word. I, for one, do not accept being called a 'bleeder'. This is the result of a vociferous, misogynistic brand of Male Rights Activism that is unfortunately appropriating others' causes to its own end. And they are letting it, meaning my sympathy for them is also limited.
Actions bring consequences. Unfortunately, these are the direct consequences of telling women to shut up, sit down, make way for men's feelings over their very real needs, and 'Be Kind'. Now, as far as I'm concerned, men can suck it up. After all, that's what they are constantly telling women to do. This is why some of us are finding our attitudes to the whole shebang are hardening, why we're absolutely sick of being marginalized and pushed out on the basis of our sex, and why we are saying 'No'.
'No' is the word. NO.