We have a temporary solution! We have started telling people we are afraid of dogs. It’s amazing – suddenly they are respectful and will actually hold on to their dog. There is no need for them to be defensive. They usually apologize.
It really works – unfortunately it doesn’t work if you’re walking a dog. 
I am not optimistic that it is a long term solution, but it does make for a more pleasant experience in the park.
I once tried telling some people, after their dog approached me wanting to “play”, that I was allergic to dogs(which isn’t true, but they wouldn’t know that). I got no reaction from them, no apology, nothing. I felt kind of bad about lying to them, but really I shouldn’t have been put into a position of having to say anything.
I don’t get why dog owners would get defensive if some people don’t want to interact with their dog in public. Are they really so insecure and in need of validation that they get personally offended if other people don’t love their dogs as much as they do?.