Whilst necessary, it isn't pretty, like men's dangly bits for that matter, far better covered up, imo.
But it's cultural Floo.
Women who dress in a Burka just see women as having more " private" bits.
Alternatively some African countries think nothing of women having their boobs on display 24/7 it's normal dress, and not private.
Imo subconsciously people (in the west) often don't like seeing a woman breast feed in public because it serves as a reminder of our animal roots.
(Deep down I think even non religious people can display that attitude, because it's learnt)
So some people feel squeamish about facing up to their roots and feel they shouldn't be offended, by having to face it in public.
IMO There isn't much more natural and beautiful, than breast feeding a baby.
It causes some people offence on a subconcious level because they are forced to see something they think of as an animal thing and that, that's where we originate.
Therefore, it can be seen as offensive. Even with Athiests who believe we evolved because it's a learnt attitude.
Our society / culture teaches us we shouldn't do (and it's not acceptable to do anything in public) something that is relating to our animal nature, which is likely to remind people they are descended from animals.
Example : , have sex, breast feed babies, give birth, go to the toilet. ( none of our functions are considered acceptable in public) it's all hidden away.
Women's periods for example, some don't even like packets of sanitary towels on show in the bathroom when guests are coming, but toilet rolls in plain sight is acceptable.
Women have been victimised in religions too, because periods are treated with suspicion as they also point to our animal roots.
Childbirth also, look at all the churching/cleansing rituals that occur before a woman is considered ' clean'..
Woman's functions are also a reminder of our animal roots and mortality.
Look at all the superstitions that has grown up around that.
Breast feeding is just another reminder that makes some squeamish, although some people may not realise why they feel that.
It's taught, subconciously.
People object specifically to boobs being used for their original animal purpose(breastfeeding), but may not object to boobs on show other than that.
There isn't that fuss on the beach.
It's all about shattering someone's self perception on a subconcious level.
That's my opinion of it.