I think that I can understand where both of these people are coming from.
There are times when I'm camping that I wish that dogs weren't allowed,but that's usually when something out of the norm has happened,such as a noisy animal,unpicked up poop,a dangerous animal,etc.
Same thing when there has been a problem with an individual child or group of children.
I will say that,usually it is because of a lack of control exhibited by their owners or parents. So maybe these people should really be looking for parks that don't allow parents or owners and then the kids and/or pets will be easier to get along with....