I didn't know this: apparently a nursing mother has a Constitutionally protected right to breastfeed her child. The following block quote describes Dike v. Orange County School Board, 650 F.2d 783 (5th Cir., 1981).
[A] teacher wanted to nurse her baby on her duty free lunch break. The school claimed that insurance provisions prohibited teachers from bringing their children onto school property, and also prohibited teachers from leaving the school grounds during the day. The trial court ruled that the mother had no right to breastfeed. In Dike, the appeals court reversed the case and remanded it for a new trial, stating that breastfeeding is a protected constitutional right. “Breastfeeding is the most elemental form of parental care. It is a communion between mother and child that, like marriage, is ‘intimate to the degree of being sacred,’ Griswold v. Connecticut, 381 U.S. at 486, 85 S. Ct. at 1682, 14 L. Ed. 2d at 516. Nourishment is necessary to maintain the child's life, and the parent may choose to believe that breastfeeding will enhance the child's psychological as well as physical health. In light of the spectrum of interests that the Supreme Court has held specially protected we conclude that the Constitution protects from excessive state interference a woman's decision respecting breastfeeding her child.” 650 F.2d at 787
Constitutional rights are not absolute, and often collide with legitimate, recognized interests. Sometimes the courts must balance individual rights with state interests. In the Dike case, the trial court determined that the state had a legitimate interest in restricting the teacher's comings and goings because of certain school policies. Although the appellate court ruled that mothers have a constitutional right to breastfeed, Mrs. Dike did not have the right to leave school to go home and nurse her baby, or to bring her baby on to school grounds.
—Elizabeth N. Baldwin, “A Look at Enacting Breastfeeding Legislation”
It's really cool what happened here. The lower court said, in an offhand way, “There's nowhere in the Constitution it says you have a right to X.” And the higher court, showing truly inspiring wisdom, says, “Look again.” Over the years, I think the U.S. courts have been better than anyone could've reasonably expected about protecting “personal” rights, beyond the political rights that the Constitution addresses most directly. It's a sometimes thing, but on a good day, the government can't just go in and randomly muck about with your private life. It's nice to be an American.