I'm torn on the subject. There's plenty of normal, natural things that still should be private, but is nurturing our children one of them?
That's because it is natural.
Where do we draw the line? Am I aloud to post pictures of myself urinating? Because that's natural too.
Natural != appropriate to show the public.
It's confounded by the multiple definitions of natural: here it just means commonplace and ordinary.
There is a public interest at work here. Breastfed babies are said to have fewer short and long term medical issues. Breastfeeding might be as important to our health (and crippling healthcare costs) as a people as bike paths, sidewalks, healthy foods, preventative medical visits, and any of the other many small lifestyle improvements which we are willing to spend many millions of dollars creating and promoting. And it costs us...a worldview adjusted ever-so-slightly back to what has been for most of our species' history perfect normalcy.
This is an important issue. Encouraging breastfeeding, which does appear to be the superior form of infant nutrition, requires that we normalize it. If we're all too delicate to see tiny thumbnails of women breastfeeding floating by in our newsfeeds, how will anybody ever survive the rather more "graphic" occurrence of it happening next to them on the bus?
I'm willing to accept bikers in far-too-revealing spandex. I have similarly learned to accept women breastfeeding. it's really not so bad once you actually encounter it...which is not something you'll ever know if you're being shielded from it by "decency" filters like Facebook's, or hearing the implied judgment that it's indecent.