Popa,
You are not alone in your discomfort. In fact, a large portion of American society agrees with your – women should nurse in private. I think this message is obscene coming from a society that has little problem with bikinis.
Breastfeeding is normal and natural. Unless you believe that women should stay home (and you can find halachic sources for this, but then be consistent and say that men should be out of Kollel to support their wives so the women don’t have to go out in public much), then women need to breastfeed in public.
So long as women are covered, I don’t understand the objection. I truly don’t. I can nurse and no one even realizes it (I did this on line at disney world – my son was in my Ergo carrier and I wore a shirt that would cover me on the sides while he was nursing).
So is your problem only if someone notices it?