19 month old DS2 BFs, in public most days, I hadn't given it a second thought really, just what we do. Still have 3 feeds a day or so. He doesn't always have his shoes on, though, so that's OK/
I can't imagine why people are uncomfortable, it is not just about an older child doing babyish things - seeing 3 year olds with dummies doesn't make people cringe (well, it might, but I see lots more of those than I do BFing 3 year olds, of which I see none. So clearly fewer people cringe at it.)
If it's because it's "sexual," then that is really, really sad.
It is a sexual act in the same way as giving birth is a sexual act - it involves the love hormone, and it involves organs that are also used for sex.
It is not a sexual act in the semi-porno, "breasts belong to men, if you are EBF you are denying your Poor Man his Rightful Place ie, your breasts belong to him and the baby is borrowing them" way. It just isn't.
The poster who said about extended co-sleeping and BFing interfering in the "marital bed," I think you were inferring that BFing interferes with the sexual relationship with a partner? Well, if it does, so what. If a man can't manage with reduced/ lower sex drive/ less sex for a few months to a year or so (realistically, most babies, even extended BF ones are sleeping through by the time they are 2) then he has his expectations all screwed up. And so do you, if you subscribe to the belief that men "need" sex in order to function. They don't. But they do like women to think they do.
And I don't even think that is all about BF, as most parents of toddlers are too knackered to shag like teenagers.