Is it ok to not greet my supervisor outside of work?

You should greet, even if it's a fake smile. These are etiquette you gotta follow, not too much but making an impact even if it's the smallest
If the eye contact happened, then you better say hi. Otherwise you can ignore him.
Were actually not suppose to here.. its an invasion of privacy
If the higher up acknowledges the other one then its okay if not then were suppose to pretend we dont know the other one.
Same if we see our doctor on the street not suppose to acknowledge him.. I seem to be the only one maybe it has to do with living in Canada I dunno.. but its actually in my jobs company policy and every other job I've had.
Opinion
3Opinion
While it might be a little rude to not say hi or like a head nod to acknowledge there presence still nothing wrong with ignoring
Its generally acceptable to do so
If he saw you that's kinda rude and weird.
Superb Opinion