It's funny that you use the adjective "dirty" to describe the bathroom that you're telling the mother to breastfeed her baby in. This speaks volumes to me. You know you're not supposed to eat someplace dirty, and you know that babies should not be fed in a dirty bathroom either. I think you know what the answer is.
Babies should be breastfed when they're hungry. It would be nice if it could always be in some private area, but sometimes the baby has the nerve to get hungry in a public place. An infant under the age of 2 cannot wait. On the other hand, a 2 or 3 year old can wait until they're home to nurse, so I don't see a real reason to do it out in public at that age.
What's with all of these people requesting blankets and spit-up cloths over the baby's face to prevent people from seeing the breastfeeding baby? Not all babies are OK with that, and I know mine always objected when I did that. Babies are not inanimate objects...sometimes they get hungry, sometimes they object to blankets over their head.
Babies make this really loud crying noise when they are not getting fed or something is being done to them that they don't like, so it's better to accommodate them in public... Who out there wants to listen to a screaming baby after all?
The best course of action if you see a woman in public breastfeeding, if you don't want to be seeing that, is to look away.