I believe it was introduced to my parish by a previous priest. He liked the symbolism and wanted everyone to hold hands as a sign of unity and love. Successive priests haven’t forbade it and usually it’s just some of the families who hold hands during the prayer. It doesn’t stretch across the aisles and I haven’t seen anyone extend hands to a stranger yet.
At my Confirmation, our current priest had all of us Catechumens and Candidates come forward and make a semi-circle behind the altar, facing the congregation, and hold hands while we said the Our Father. It was unexpected and a little awkward, but it really was a very special, holy moment. Everyone seemed lit by holy light as we stood around the altar, bathed in all the light from all the Easter Vigil candles.
I don’t see anything wrong with a family holding hands as they pray together, either at home around the dinner table or at Mass. Groups of people pray the Our Father together all the time in the Rosary or Chaplet. Families should be praying together at home, asking God to give us our daily bread, to forgive each other, to have God’s will done here in our home as well as on Earth. Why is it any different to do it at home and not at Mass? We are all God’s family, and we can pray to Him together and separately, holding hands or not.
I’m not saying people should be aggressively grabbing your hands, but I find the near-hatred of hand-holding at Mass kind of strange. I haven’t yet got my kids in the hand-holding routine yet, but I would like it if they did. If a stranger extended their hand to me, I would be very happy to take it. I would feel honored and welcomed by them as part of our spiritual family.
If the priest hasn’t forbidden it, I say let those who like it, participate, and those who don’t, just turn a blind eye and focus on your own prayers.