Breastfeeding has two major single-issue advocacy groups. The first is La Leche League, founded in Chicago in 1956. It has no particular political stance. The second is Breastfeeding USA, founded in 2010. It has a very slightly liberal stance.
My mother was an LLL Leader for 35 years, and is a founding member of Breastfeeding USA.
The strange thing for me in the US is that the left doesn't seem bothered by it. They are usually all up to point out arbitrary social constructs but this isn't an issue for them? Am I missing something?