Whether it's a child or a dog, and the child or dog is being a nuisance to other patrons of the business, then it is irresponsible for that parent of child/owner of pet to not do something to try and minimize the noise.
Kids will be kids and pets will be pets, but PLEASE consider the other people in the establishment when your child/animal is being loud and/or obnoxious. I have kids, and we consider others before we even leave the house, by packing up small things for the kids to do to keep them entertained while we are waiting for service and food.
If your kid is screaming, politely get up from your table and take the kid for a walk, let them go run around outside for a few minutes, and continue the screaming fit somewhere other than right next to people who want to enjoy their meal. Easy, and polite.
Case in point. We went to Santa's Wonderland a few weeks back. It was freezing cold. There was a mom who had a toddler, maybe 18 months old, who screamed the enter hayride. Why? Because the mom dressed him for warm weather and the kid was freezing. We put up with this screaming fit for the entire 35 minute hayride. Now, after paying $60.00 to ENJOY the hayride with our family, we certainly did not get the full enjoyment out of it since we had to listen to the kid the entire time. It wasn't the kids fault, we realized that, and even offered our blanket that we brought from home for the mom to wrap around the kid. She declined our blanket and the kid froze the entire time. Bad parenting = bad hayride.