Someone I know once complained to my wife that I walked past him in the street and didn’t even say “Hello”. I must have been in another world, thinking about something far removed from my present surroundings. I did have the sense and good grace to apologise and to assure him that I usually greeted people, even – as Jewish ethics require – greeting them before they greeted me.
Rav Huna said that if you fail to return a person’s greeting it is as if you have robbed them (Ber. 6b).
I know that Pir‘kei Avot (3:7) is not in favour of a person interrupting their study in order to comment on their surroundings, but this is probably a warning against lack of concentration.
As a general principle one should never regard the other person as if they did not exist – a piece of advice particularly relevant in an age when we tend to ignore the dignity and conscience of people we don’t agree with.
One should never forget the famous rabbinic interpretation of the Four Species of plants which we take on Sukkot. The community of Four Species requires the tall and the short, the fat and the thin and so on. This is symbolic of the ideological community; there is no reason why everyone should think alike.
If I believe the other person is wrong, the answer is not to pretend they don’t exist but to sit and talk with them and if necessary agree to disagree.