You are missing the point. When the priest says "Let us offer each other a sign of peace" what do you do? Do you not acknowledge your neighbor as Christ did? Not only are we at Mass to worship God but we are also asked at Mass to be like Christ.
"You are missing the point. When the priest says 'Let us offer each other a sign of peace' what do you do?"
It's not an issue for me as I do not attend religious services with Roman Catholics. In the Orthodox Church, the exchange of peace is normally exchanged at the altar during the Proskomide as follows:
"Priest:
I love You, Lord, my strength. The Lord is my rock, and my fortress, and my deliverer.
(At this time it is customary for the kiss of peace to be exchanged.)"
But to answer your question more directly, you introduced a false premise, that being that I am at the liturgy for any purpose other than worshipping God. That to me is a very strange idea. Before I became an Orthodox Christian, I used to attend Novus Ordo masses and, quite frankly, I found the exchange of peace in the nave a distraction at best and a possible cause of scandal at worst.
"Let us offer...." is an innovation, or at least, after 400+ years of NO kissies, huggies, or whatever, ...now, suddenly, this is important?
A smile will suffice.
Even the most lit-wonk poofter activist in the US, Rembert Weakland, stated that the "sign of peace" is in the wrong place--it should occur at the BEGINNING of the Mass.
But to put a twist on the song: If Rembert's for it, WE can be against it, without fear...