However I'm entitled to choose life without one, and their lifestyle choice should not trump mine. I don't want dogs to touch me, lick me, or come close enough to me or my children to make me (or them) feel uncomfortable, intimidated, or upset. Why is that so hard to understand?
I agree with this totally. I had lots of pet dogs when I was young, loved them, and was never nervous about other people's dogs ... until the day a neighbour's normally friendly dog tried to sink her teeth in my throat. I really don't feel the same way about dogs now, especially dogs I don't know. I am especially sick of dog owners who let their dogs lunge at me, leap up at me, lick me, try to smell my crotch, or leap on or sniff at my children, while saying "Don't worry, he/she is just being friendly" because if they can't stop their dog doing irritating things to strangers, they are obviously not in control of it and there is no guarantee that it won't bite. In addition, having seen elderly and not-so-elderly people being knocked over by running dogs (including one who ended up with a badly broken leg due to being knocked over awkwardly), I do not underestimate the potential risks from being knocked over by a dog.
In short most dogs are lovely, parents please don't teach your children to fear them.
I am not instilling a fear of dogs in my children but I am most certainly teaching my children not to get close to dogs they don't know because I think this is an important life skill. OP: I think you were definitely NBU to want to put a distance between you and the dog.
It would be really nice if dog owners realised that other people may not find their dogs as cute and loveable as they find them ...