People get weird about it because we as a culture have major hangups regarding sex and sexuality, and breasts are seen primarily as sex objects. And that's precisely *because* many of us aren't regularly exposed to a mother in the act of feeding her baby, whereas breasts are displayed in a sexual context absolutely everywhere you look. We're trained to see breast-as-sex-objects as the normal function of breasts, and breast-as-baby-support-system as a sort of secret alternate use of them.
The only way this will change is if people become accustomed to seeing mothers nurse their children. If you're exposed to something regularly, it stops seeming strange or abnormal. The more we support women in their choice to nurse their children, the more people will see it as a perfectly normal, unremarkable thing.