Unfortunately when people think about breast and indecency that is due to the women's bodies being sexualized and objectified. It is so embedded in some cultures that we don't even realize what we are doing or why it makes us uncomfortable.
Indecency is not universal however. Look at African cultures that allow women to walk around all day without a top. They do not see the breast as sexual but rather essential to life. No different then an eye is for seeing, and the nose is for breathing.
In this case women should be able to, but that does not mean that they have to if they do not want either.
I'm always somewhat irked in public breastfeeding debates that will excuse public breastfeeding as long as the woman makes an effort to cover herself up. Now, some women are more comfortable being discreet, but other women (myself included) find that severely hampers the breastfeeding. To expect a woman to always cover up is unrealistic and unfair.
Women have the right to feed themselves anywhere and however they want- how is feeding their child different? It is a natural need, and no mother should have to cover up just because a few people object to it. It's a natural born right of a woman to feed their child wherever they want, and however they want.
Despite society's view and sexualization of breasts, their biological and evolutionary purpose is for the feeding of infants. The act of feeding harms no one and "concerned" parties can simply look away if it bothers them. Therefore, women should be allowed to expose their breast to feed their child in public.
I fed both of my children in public. I covered up. Everyone knew what I was doing. My child ate. People for the most part were not offended. There will always be someone that will complain.
I did not use a cover in my home, but I still did not expose my entire breast when other people where around.
My breasts are my private parts, and should be treated as such at all times. Private parts are defined as the parts of the body covered by a swim suit or underwear.
I now face the problem that my sister feels that she should breast feed while exposing her entire breast infront of myself and my two sons who are in elementary school now. It may be her "right" to expose herself. However, it is my right to decide what my children will be exposed to. I will not expose myself or my children to her private parts.
My sister's choice to breastfeed without a cover turns into my choice to not be around her. It is very sad that her and my relationship as Aunts takes a back seat to her need to "not" cover up her private parts.