I am pregnant with my first child but have worked as a nanny for years. I am always surprised when I see people changing their babies/toddlers nappies/clothes in public. For example I attend a playgroup twice a week and often a toddler will have wet themselves or a baby needs changing and the parents (different ones) think nothing of changing them in front of everyone.
You wouldn't get changed yourself in front of a group of people so why is it ok for a baby/toddler to be seen?
I have never, in my 15 years of nannying, had to change a nappy/wet toddler in front of anyone.