Interesting read - and I remember a few years back when I walked by a playground and the sign said that unaccompanied adults without children weren't allowed in the playground. That sure is backwards compared to what I remember as a child!
I had a urgent shoot for a client a few years back at a theme park and called to get permission the day before, but had to go without waiting for clearance as a tropical storm was coming and I had to get the shots. I saw the main security guy as I was shooting and instead of waiting for trouble, I went up to him and talked to him. I explained what I was doing and he was really cool about it and he only said one thing, "Don't take pictures of other people's kids."
The sad reality is that there are a number of people out there selling fear to parents. There really aren't 50,000 sexual predators online at any time, nor are there 50 kids abducted in the US each day, or razor blades in apples on Halloween. These and many other false statistics are used to coerce parents into buying things they don't need and have the side effect of making parents completely paranoid. I work with the law enforcement groups who track predators and missing persons, so I'm not just saying this off the cuff.
The second reality is that a lens like the 300 f/2.8 is going to attract a lot of attention, good and bad. Most of the time, mine has been okay, usually someone annoying asking me lots of questions.
I think AcutancePhotography's advice of not escalating the situation is good, and it also helps to understand that most parents are convinced that there's a kidnapper or pervert lurking behind every tree. Putting yourself in their shoes for a moment and helping to reassure them is usually a good strategy.
It sounds like the OP did try to do some of that, so in some cases people are just jerks and you can only do what you can do. The people that you really need to be wary of are police and security. Working with that group as well, many of them are convinced that anyone taking photos of a public building and especially anything deemed "critical infrastructure" is up to no good. Cooperate, but know your rights.