I have no problem with breast feeding in public - its perfectly natural and no one should feel ashamed of it.
Nappy changing is totally different story - from practical perspective, just because the contents are currently wet doesnt mean that at any moment the child won't suddenly have a poo as well - which is not pleasant. I don't think it is unreasonable to expect toilet related business to be done in the toilet and nappy changes to be conducted there as well. No child is so important that it cannot possibly not wait 30 seconds to go to the loo and be cleaned up in there.
I am not a parent, but an observation I would make is that many friends who are parents say 'oh its different when its your own childs poo' - well I'm sure thats correct as they're the ones who've spent years dealing with it. I on the other am not used to seeing or smelling your childs bowel movements and have no desire to do so. This is the point at which you are inflicting your child on others.
As others have noted, at what point do we draw the line for nappy changes? Is it babies, toddlers, older children with disabilities who still need them, adults with incontinence problems or even that slightly odd community of adults who wear them for sexual pleasure - after all, its just a nappy change.
The other point I'd note is that in this day and age where we are hyper aware about the paedophiles lurking under every bed (if you believe the tabloids), I am astounded people would willingly want their childrens genitals on public display. How would they react if someone then got a phone out - would they assume photos were being taken? I could see a potentially very difficult scene ensuing as a result...