Not having children surely doesn't disqualify anyone from noticing some of what works and what doesn't work with respect to teaching kids how to deal well with the rest of the world. Everyone has access to the knowledge they gained watching their own parents raise them as well as different approaches they see used by friends and relatives. Thought that kind of "you have to be one to qualify" thinking went out with "You can't be a good drug counselor if you weren't a heroin addict first." Guess some people still believe that.
Having been a school psych for a chunk of years, I noticed a long time ago that by far the most disturbed and frightened/frightening kids I meet are not the ones from abusive homes but the ones from homes where the parents have abdicated and left their kids in control.
I don't think most people, childless or not, automatically judge when they see a whining, crying kid in a store (heck, I was one of those "I want that CANDY" kids myself. Come to think of it, sometimes I still am---although quieter). Kids whine, kids cry. The issue for most people, I think, is whether the parents are letting those kids ride roughshod on the people around them. And since we all share the same space, I think everyone has the right to weigh in on that one, and that all that info is genuinely worth considering. I really do.
"My predominant feeling is one of gratitude. I have loved and been loved;I have been given much and I have given something in return...Above all, I have been a sentient being, a thinking animal, on this beautiful planet, and that in itself has been an enormous privilege and an adventure." O. Sacks