One of the problems I see in the Catholic Church in general is that we often don’t know the people we worship with. In a smaller church – like many Protestant churches – everyone knows everyone else. I think that something like a greeting that helps us connect with each other before we join together to pray is a good thing.
While you are right regarding our not knowing the folks with whom we pray, the context of the Holy Sacrifice of the Mass is not the time to meet and greet. Protestants do not have a concept of liturgy, per se. For them, worship is pretty much a lengthy bible study, with a sermon and music thrown in for good measure.
However, for Catholics, worship is something very different and something that is out of the ordinary. At Mass, we enter God’s time. The veil between heaven and earth is lifted and we enter into the divine Majesty of the presence of God. During the Mass, we are engaging in something greater than ourselves. Yes, we are worshipping as a community; but, the community is not the crux of the Mass. It is the Holy Sacrifice of Jesus. We join Him and unite ourselves to Him.
This is what we need to concentrate on, according to the former Joseph Cardinal Ratzinger:
The liturgy is not a festivity; it is not a meeting for the purpose of having a good time. It is of no importance that the parish priest has cudgeled his brains to come up with suggestive ideas or imaginative novelties. The liturgy is what makes the Thrice-Holy God present amongst us; it is the burning bush; it is the Alliance of God with man in Jesus Christ, who has died and risen again. The grandeur of the liturgy does not rest upon the fact that it offers an interesting entertainment, but in rendering tangible the Totally Other, whom we are not capable of summoning. He comes because He wills. In other words, the essential in the liturgy is the mystery, which is realized in the common ritual of the Church; all the rest diminishes it. Men experiment with it in lively fashion, and find themselves deceived, when the mystery is transformed into distraction, when the chief actor in the liturgy is not the Living God but the priest or the liturgical director.
Meeting and greeting can happen in the vestibule before Mass or after Mass, but not during.
When my pastor celebrates Mass, he comes out in an alb and greets us, prior to the start of the liturgy. He asks us to introduce ourselves to each other and then he asks if anyone is celebrating a birthday or an anniversary. Then, he asks if anyone is new to the parish. If so, he then asks from whence they’ve come.
It does grate on me to have to do this. I try to sit as far away as possible so that I won’t have to be part of the meet and greet fest. He’s trying to build up community and he means well, but, I think it’s the wrong approach to take.
When my PV celebrates Mass, he spends time in front of the Blessed Sacrament before the liturgy and then goes and vests in the sacristy. He then retires to the back of the Church, rings the bell and the entrance profession begins.
Whatever socializing is done happens after Mass.