I don't want to go again into the original significance of the Pax at its traditional place in the Roman Rite; in posts some time ago I showed conclusively that the idea was that a liturgical Kiss concluded and sealed what had just been done (here, in the case of the Eucharist, consecration and oblation). No; I want to put some question marks against the significance assigned to it in the Pauline rite.
"The faithful implore peace and unity for the Church and the whole family of men and express mutual charity with each other, before they share one loaf". MR 1969 IGMR para 56 b.
I doubt whether it would be easy to find much patristic support for the thought that Christians ought to be concerned for the unity of the human family qua unredeemed - for humanity before and without Christ; you don't have to be a Calvinist believer in the massa damnationis to have read your New Testament and to know that 'brethren' are brethren because it is Baptism that makes one a co-sharer in Christ's Sonship so that one can cry "Abba".
But my real query is about the logical link asserted between the Kiss and the eucharistic sharing in One Loaf. I do not understand why those who are admitted to the Kiss can be excluded from the Loaf ... or why those to be excluded from the Loaf are admitted to the Kiss.
On the Solemnity of SS Peter and Paul, the Orthodox representative was the first to receive the Kiss from the Pontiff. And because, down there in the congregation, the the Kiss is unpoliced, there can be no doubt that it very commonly occurs that non-Catholic and even unbaptised visitors at Mass are given a warm greeting at Pax time (even though the paragraph quoted above technically suggests that the Pax is confined to the fideles).
Old-fashioned worshippers are sometimes opposed to the Peace because its faux-friendly hypocrisy interrupts their private piety. I have some (limited) sympathy with this, but I think there are graver and theological objections to the customs which have grown up. Or at least, questions which need answering about them.
[I quite often seem to be misunderstood. I am not arguing for indiscriminate communion but against indiscriminate Pax.]