My understanding of the kiss of peace is that whilst one aspect is a show of fellowship and love, it is primarily an act of fulfilling the command to reconcile with our brothers before approaching the altar.
Whilst this can be done symbolically by exchanging the sign of peace with those immediately around you, it seems to me that if there is someone in the congregation against whom you have a particular grievance or judgement, then it would be appropriate to walk across the church to make peace with them. (- Not by discussing the matter or “talking it through” but simply by offering the sign of Christ’s peace with the humility and unconditional forgiveness that we receive from Christ). After all as Catholics, we deal in what is real and concrete, not merely symbolic and wishy-washy.
So it seems to me that this is an important and integral part of the liturgy and I would definitely not want it to be omitted.
However, I do sympathise with those people who find it distracting. To have the sign of peace directly after the consecration, with the body & blood of Christ sitting on the altar, does seem to me a very strange time to do it, and I am tempted to think it completely inappropriate.
The best solution that I can think of is to move the sign of peace to a more appropriate point in the liturgy. The time that suggests itself is after the Prayers of the Faithful and before the Offertory. This seems to make more sense from every aspect. This is the point at which we pass from the Liturgy of the Word to the Liturgy of the Eucharist. The readings and homily having helped to concentrate our minds, we now prepare ourselves to approach the Altar by first making peace with our brothers.
To me, this seems to be the best way to do things. But before you all hail me as a liturgical genius or indeed condemn me as liturgical innovator, I should explain that this is in fact an existing and authentic liturgical practice which is part of the Ambrosian Rite which dates from at least the 4th century AD and is still in use in Milan today.
With Love,
Simon.