I think you've immediately contradicted yourself by giving an example of women walking around topless not as a sexual display and not with the intention of antagonising people. It also doesn't match the next category you give - a functional context for medicine or education.
Nudism seems to rebut your line of argument. It's also a rather bad example for arguing that no restrictions should be allowed on breastfeeding because nudity is extremely restricted in public, allowed only in a few places.
No, the point is that sexualisation and functionality are not comparable, yet it is largely down to context. Nudism serves neither, but it is removed from the sexualised context, and due to its unique context is acceptable. That too, for for some being nude is the function in itself.
Medicine and education are non-sexualised and acceptable.
"
**** walking" is sexualised even though it's antagonistic in nature which is why it's unacceptable. In fact, it's antagonistic because it's sexual, but you know that.
A topless art-model is serving a function, even though it could also be considered somewhat sexual but its function helps keep the lid on it. But, it is largely down to the setting and the immediate company.
There isn't a complete black and white here.
Breastfeeding isn't sexualised and is -- or at least should be -- completely acceptable.
As we've been over, the problem stems from when it crosses that boundary between sexualisation and non-sexualisation. Completely removing a top in a public setting to that end crosses that threshold. Doing it discreetly however, does not. People have a valid right to object if a woman is making a spectacle of it. If it's being done tastefully, then the prudes and snobs are the ones which have the issue, not the mother.
You could point out that as the mother is breastfeeding, being completely topless or not shouldn't be an issue as she is still serving a function but the point is, she is able to do so without going to such an extreme. A topless art-model on the other hand is expected to be so even though given the context, it is also functional.