I haven't ever heard anyone in real life say it was disgusting though have heard the arguments about it many times.
Boobs are boobs some are attractive some aren't, a baby sucking on one is normal, a grown adult sucking on one is a bit fucking weird. Drinking milk from a cow, sheep, goat is even weirder especially coming from people that think a baby feeding on their mothers milk is "disgusting".
I have been in situations where it has been super awkward. You will be generally looking in a direction say at the specials board on the wall at the other side of the restaurant, a menu of a coffee shop or just thinking and not really looking and you notice a woman is giving you the evil eye so your like "fuck you I'm not looking at you", then a babies head pops up. Then once you know they are breast feeding and feel awkward for the moment prior by trying not to look you end up looking more making it super awkward. I think that is a possible reason in that they don't want to feel awkward or embarrassed.