The problem is that we live in a society where rules of modesty are so deeply engrained we can't simply turn them off when something like a breast -- which has two functions -- is contextually used for its other purpose.
Fact one: Breasts are a sexual object. They have evolved to resemble the buttocks and are also highly-charged sexual symbols for men in our society due to the modesty factor.
Fact two: Breasts are used to feed newborns.
People should respect the fact that a small child will need to eat. However, mothers need to also be considerate that other people may genuinely feel uncomfortable around such behaviour because of the implicit rules of society.
Everyone understands that babies need to eat and no-one is criticising that fact. The problem is the naked breast itself because it is such a charged sexual object which creates cognitive dissonance and observer discomfort in others. That too, it very much feels like an invasion of intimate privacy to "catch an eyeful"
To me, it reads as if some commentators on that news-piece (and a subsequent link to that wonderful bastion that is Buzzfeed) are misinterpreting the difference between breastfeeding being illegal (which it is not and only a crank would demand such a thing) and the simple consideration of others. This can be summed up by the recent issue where a restaurant owner was actually bullied in to apologising when they asked if groups of breast-feeding women could use alternate facilities available rather than upset other patrons. I don't see any discrimination here, only a polite request.
If there are facilities provided, such as a private room to go breast-feed (and not a smelly toilet), I don't understand why there is such a stink. It would be discriminatory if they were disallowed from feeding outright, not through being asked to be courteous. If there isn't facilities available and the only option is to whip some bosom out in full public view, then fair enough that's how it's got to be. But there's a difference between doing this brazenly or discretely.
The freedom to do what we need and want in this life also needs to be balanced by responsibility. The responsibility here is to be aware that it makes other people uncomfortable due to the schism in perception of the breast as a sexual object and a maternal one whilst also feeling invasive of privacy. Just because someone is a parent and doesn't see the breast as sexualised any more, doesn't mean that others will not. Nor will others stop feeling as if they're invading personal space by witnessing such an act.
At the end of the day, the offended people in question probably could do with a little growing-up as people ultimately choose to get offended or not. Indeed, someone breastfeeding their child really should not appear on the list of "things that bothered me today" whereas "that chap that nearly hit me with his car as I was crossing the road earlier" actually should. Yet, society being what it is and people being the conflicted creatures that they are means that that is and can only ever be an ideal. A teenage boy for example isn't going to suddenly stop finding breasts fundamentally alluring simply because a baby is attached. The naked breast in our society isn't normalised. It's taboo and intimate.
For me, it simply comes down to consideration. People should be considerate that a child needs to be fed and that comes before anything else. But also, mothers should -- and I imagine for the most part they are -- considerate of other people around them. If a mother is doing it discreetly, rather than brazenly flopping some boob out wholesale before attaching their child to the end of it whilst making suggestive eye-contact, then let them be. In the picture above for example, I see a child feeding, but it is discreet and completely inoffensive so why the need to cover? Let them be! If a mother is doing it to antagonise -- which if a child is demanding food from them, I hardly think will be their first concern -- then they are the one with the issue, not the silly prudes.
It's almost like smoking at a dinner-table. If you know others won't like it or it will put them off their meal, don't do it or if you must, just be considerate about it and don't go blowing it in their faces.
The bottom line is that a child cannot be reasoned with and if they need feeding, that takes precedent over the feelings of a grown individual. Kicking a mother out for feeding their child is just wrong as was covering her up in the above photograph.