And now for the old man view of this:
1. Yes, babies have to feed, but that does not mean that babies have to feed in restaurants while other patrons are enjoying a meal they are often paying dearly for. In addition, babies don't feed non-stop, so this woman was quite capable of having someone else pick up her takeout meal while feeding the baby at home or waiting until after the baby's feeding to go pick up her order. But I'm sure that would inconvenience her, so that's a no go. Alternately, order your takeout meals from a place that delivers.
2. Babies and small children in restaurants other than fast food joints where most patrons are in and out in minutes is inconsiderate in my view. Just because you have a "right" doesn't mean that it's appropriate or considerate to exercise it at all times in all locations. The me/now mentality of some in modern society is why you have so much "rage" out in public. One of the "sacrifices" of starting a family is that you give up some of the adult things you used to enjoy until such time as your children can fully participate and enjoy those experiences.
3. I come from an era where people didn't display their bodily functions in public for all to see and "enjoy". I've had the good fortune of sitting in a restaurant and hearing a patron horking away into a napkin for minutes on end rather than excuse themselves to the bathroom to take care of whatever it was. Likewise, enjoying a meal and having someone close by sneezing and coughing as if they were about to expire from some tropical infection, with no consideration for anyone else in the restaurant. For me, if I'm sick or not 100%, I don't inflict my problems on others - I stay home.
4. For me, it has nothing to do with sex or body parts or whatever else prudish someone wants to attribute it to. It has to do with consideration for others you're sharing the planet with and attempting, as best you can, to be respectful of others before you think of your own comfort and convenience. On that note, I never would have intervened with the woman if she's started breastfeeding in a restaurant while waiting to pick up a takeout order. It's not worth my time to get upset and confrontational about the actions of others in that way.