There once was a time in the United States, when breastfeeding a baby was done, in public or not, because that was the only way to feed babies. Then, along came the corporate production of bottles and formula, and mothers who chose to have their babies delivered in the hospital, were now having their choice of breast or bottle feeding thwarted by the 'good doctors' who supported the industry of formula.
Breastfeeding is NOT an issue of morality. Breastfeeding happens to be a form, and the MOST NATURAL form for feeding an infant. Let me ask this question: Does the public get squeamish because animals suckle their mother's teats in public?
Breastfeeding in public does not necessarily mean that you whip your breast out in front of a trillion watchful eyes of all ages. There are as many ways to breastfeed discreetly as there are mothers and babies. I used to wear a poncho and tuck my baby under without anyone knowing the difference. In the summer, it would be a light shawl or poncho and no one knew the difference. Other times, I would step into the bathroom and feed them there. Nowadays its even easier-there are 'nursing rooms' or sitting areas in many bathrooms. There are even family bathrooms in public places.
Anyone who feels this is a naughty thing or immoral really needs to take a check in regards to how they happen to view a woman's breasts. If it is as a sex object, then of course there will be negativity regarding exposing the breasts for an infant to be nourished. If it is as a natural part of the human cycle, then of course there will be positive support in regards to nourishing the little one.
Interesting question, alvairs!