Kids are dogs that eventually learn to talk. If both are trained properly, then I have no issue being around them in public, but the second I'm asked to put up with someone else's kid/dog's bad behavior. Nope. Keep it at home if you can't be bothered to do your job and teach them how to act.
People always told me how well behaved my kids are...same when I had dogs. It's just not that hard to tech them basic manners. Now, we all know some little kids (my 3yo son) will freak out and not listen and other parents get that, but when it's non stop and the parents ignore it? That's a different situation. The world doesn't revolve around you and your kids. People can get pissed if they invade their space and it's your job as a parent/owner to fix it.