I'm not going to greet a random guy I didn't recognise in the park
Why exactly won't you greet him?
I do not greet strangers.
If you don't want to greet strangers you don't have to.  You don't have to show recognition to people you don't know well. Greeting every stranger you pass would be cumbersome.
I think it is bad that people call cops when they are scared and I will call cops on him if he scares me.
I think you are doing the right thing when it comes to scary strangers. You need to follow your gut and stay safe.