I try to exercise appropriate discretion. But, I will look a man straight in the eye and not flinch. That has sometimes gotten me accused of having a staring problem. Whatever, if you can't stand being looked at, don't come out in public.
In some countries its considered rude to look at people. I think that's a low social condition for a country to be in. In America, at least the old west, people were never afraid to look each other in the eye and maintain it for more than one second. Most people won't even look at you on the street now. It's very rude not to acknowledge someone, at least by traditional American standards.
When you pass someone on the street, you should look them in the eye, smile and nod or say hello. The world would be a better place if so many people weren't afraid to do that anymore. But, psychologists have trained everyone not to talk to strangers. So, nowadays, people won't even meet their neighbors.
We should all get back to the old customs and start to be friendly again.