Well I think there are a couple layers to this discussion.

First there is a standard of reasonableness that has to be applied. It isn't reasonable to expect an overweight individual to only leave the house at night. However I would say that it is fairly reasonable to ask someone who is breastfeeding to plan ahead and pump beforehand so they can use a bottle, to breastfeed in the designated area, or to use a thin blanket to cover themselves.

I don't think the act is mean to be shame filled, I think it goes back to respecting public spaces. For example, some people are uncomfortable with exuberant public displays of affection, even if they are perfectly within the law (no nudity or lewd acts).

If you saw 2 people making out in public, whether their were kids around or not, it wouldn't be that abnormal for you to chide them and ask them to be respectful to the people who might not want to see that.

Does that mean that you are shaming them, you think sex or physical affection is gross and disgusting? No, not at all. But you would rather not see that in a shared public space.

For me the issue is simply one of courtesy and respect for others and not a personal attack on motherhood, sexualizing breasts, shaming or anything else.

When I am in a public place and see a woman breastfeeding it makes me uncomfortable. I feel like I am intruding on a private and intimate moment, which I now have been thrust into against my will. I don't think it is sexual, but it is private. When it happens I typically just get up and leave wherever I am, because unless that is my wife nursing my child, that isn't something that I need to see.

But my personal feelings aside, I think it is just a shame when we reach a point in society where we no longer care about common courtesy.