Have you ever tried wearing sunglasses? No one knows where you are staring in them. Other people swear by aluminum foil hats.
Sure, I’ve been told I’m scary-looking (which in my case may be a euphemism for ugly), but since I also take no pleasure in scaring people, I’ve cultivated a habit of smiling whenever I catch someone’s eye.
Seems to work pretty well, with the added benefit that I haven’t found myself in one of those stupid (and typically alcohol fueled) Monkey Dance stare downs since I was a much younger man.
Incidentally, I suspect that those of us who were lucky enough to have been raised in an environment which included a minimum of physical violence are the same ones who profess to be unfamiliar with the MD phenomenon.
I learned in 4th grade how to deal with this. You just flip your eyelids back so that they’re stuck with the inside facing out. The other guy either looks away, or starts laughing. If it’s a girl, she gets grossed out.
Guys. The OP was stabbed in a stare-down contest a few years ago.
My husband’s boss used to puff up his chest and scowl every time he walked by my husband. One day, my husband asked, “You feeling alright?” To which the boss barked “Of course!” My husband replied, “You don’t look so good.” Took the wind right out of his sails.
You guys are making me think of the dog in the animal control jail, who was staring Bitzer out of countenance, in the Shaun The Sheep movie.
The best defense is a good offense. I two Alka Seltzers in your mouth so you start foaming like a rabid dog. Scares the hell out of them. 
Look away and laugh.
Look them in the eyes, laugh and then go about your business.
Suddenly throw your arms out and go wide eyed in phony/comic shock, laugh and go back to what you were doing.
Big wolf smile, keep looking them in the eye, ask if they need something or if there is a problem.
Or as above, look around and behind you for a second.
Whenever anyone looks at me in any way, even just in my general direction, I deescalate the potentially aggressive situation by calmly walking over to them, then pull out the waist of their britches, and drop in my ferret.
…it also gives my ferret, Mr. Nippy, a little exercise. When he finds anything roundish and bite-size: *pop goes the weasel. *