Absolutely the right take. Nobody would be mad at Ana for saying

"haha hey guys, 'birthing person' is important in legal and medical contexts when you are speaking about a group of people and don't want to exclude NBs and trans men, but you're not supposed to just CALL me a birthing person day to day 😂"

We're mad because she has been doing just a standard reactionary rant, so much so it's getting shared by right wingers. Absolutely stupid.