Although not a part of our culture, that at least would be Biblical:
It was the widespread custom in the ancient western Mediterranean for men to greet each other with a kiss on the cheek. That was also the custom in ancient Judea and practiced also by Christians. In the Gospels, greeting with a kiss was also the custom practiced by Jesus.
However, the New Testament's reference to a holy kiss (en philemati hagio) and kiss of love (en philemati agapēs) transformed the character of the act beyond a greeting. Such a kiss is mentioned five times in the New Testament:
Romans 16:16 — "Greet one another with a holy kiss" (Greek: ἀσπάσασθε ἀλλήλους ἐν φιλήματι ἁγίῳ).
I Corinthians 16:20 — "Greet one another with a holy kiss" (Greek: ἀσπάσασθε ἀλλήλους ἐν φιλήματι ἁγίῳ).
II Corinthians 13:12 — "Greet one another with a holy kiss" (Greek: ἀσπάσασθε ἀλλήλους ἐν ἁγίῳ φιλήματι).
I Thessalonians 5:26 — "Greet all the brothers with a holy kiss" (Greek: ἀσπάσασθε τοὺς ἀδελφοὺς πάντας ἐν φιλήματι ἁγίῳ).
I Peter 5:14 — "Greet one another with a kiss of love" (Greek: ἀσπάσασθε ἀλλήλους ἐν φιλήματι ἀγάπης).[1]
The writings of the early church fathers speak of the holy kiss, which they call "a sign of peace", which was already part of the Eucharistic liturgy, occurring after the Lord's Prayer in the Roman Rite and the rites directly derived from it. (Wiki)
I am very comfortable with the sign of peace. Justin Martyr wrote of it as part of the mass in his apologia to Caesar.
What distresses me is that the Lamb of God is always begun before everyone has finished with the sign of peace.