Instructions to greet other believers with a holy kiss appear in Romans 16:16, 1 Corinthians 16:20, 2 Corinthians 13:12 and 1 Thessallonians 5:26. We don’t know much about what the holy kiss was like, other than the fact that it was a friendly greeting. From the context of the Bible, it does not seem to be romantic. And the Bible says nothing about holy kissing on the lips. Perhaps it was like the kiss on the cheek that French people use to greet each other today?
Regardless of the exact nature of the holy kiss, Paul does not mandate that we kiss each other each time we greet, as a command for churches of all time. It would appear that the Biblical principle is that believers should greet each other warmly. In the Greek culture of New Testament times, that greeting was apparently accompanied by a kiss. In America and Great Britain today, it is accompanied by a handshake. And other cultures signify greetings in other ways. Therefore we should not feel bound to kiss other believers, regardless of culture. In some places today, kissing would be inappropriate. In other places, a modest kiss on the cheek is normal. Therefore, Christians today should keep the Biblical principle behind the holy kiss (greeting other believers warmly), even if they do not actually kiss.