I'm embarrassed to say that I used one of these in the early weeks. I lived in Singapore and Chinese culture means public nudity is forbidden, and Malay Islamic culture dictates that women if they do breastfeed do it in women-only settings behind closed doors. I only ever have seen 4 women breastfeed (white and Japanese women, never seen a Chinese woman) and they all used bibs.
There are also no laws safeguarding your right to feed and there are regular stories about women being asked to move on.
I'm the least shy person I know and couldn't care less who saw me, but in the vulnerable first weeks I was out and about alot (fed in public on average twice a day) and just didn't want any aggravation. It's not the idea of feeding that antagonises some people there (they are enormously child friendly), it's the nudity. It's a mix of fifties Britain, evangelical Christian, and Chinese culture there. Not public breastfeeding friendly.
But I hated my self for using one and feel PASSIONATELY that feeding should not be something hidden away. So I stopped using it, and you know what, it was fine. No one asked me to move on (mind you, I have that look) and let me get on with things. Partly, I think they let crazy Ang Moh (white) woman do what she likes.
My breastfeeding experience in Singapore ended up being fine. I was only asked to move once, by a security guard, and I ignored him. The only tutting I ever got was from a fellow patient in the children's centre in the hospital!
I'm still a bit funny about feeding in front of my 98 year old grandfather though.