Personally, I hold hands during the Lord’s Prayer. That was a novel gesture to me when my family moved to Michigan when I was 11, but quickly it became a natural gesture. It’s now much more widespread.
Some more traditionally-minded Catholics don’t hold hands during the Lord’s prayer and argue against others holding hands, suggest that holding hands derives from a Protestant practice and note that is not called for in the General Instruction on the Roman Missal (GIRM).
Here’s one such example of an argument against hand-holding: aleteia.org/2015/07/06/the-lords-prayer-during-mass-should-we-hold-hands-or-raise-them-in-the-air/
I think there is solid basis in the norms for celebrating mass to support the holding of hands during the Lord’s Prayer.
First, the General Instruction on the Roman Missal does include language on “The Duties of the People of God” that, to me appears to be an exhortation to corporate charity. For example, section 95…
“95. In the celebration of Mass the faithful form a holy people, a people whom God has made his own, a royal priesthood, so that they may give thanks to God and offer the spotless Victim not only through the hands of the priest but also together with him, and so that they may learn to offer themselves. They should, moreover, endeavor to make this clear by their deep religious sense and their charity toward brothers and sisters who participate with them in the same celebration.
Thus, they are to shun any appearance of individualism or division, keeping before their eyes that they have only one Father in heaven and accordingly are all brothers and sisters to each other.”
How are people to “endeavor to make this clear?” Through “deep religious sense” and “charity toward brothers and sisters who participate with them.” Does that mean that people are just supposed to “feel” really strongly toward their neighbors? There’s lot going on in the minds of the people described in Section 95. It seem to me that holding hands is a perfectly “organic” way to express that charity toward one another (to cite Sacrosancrum Concilium 23).
The next section of the GIRM also contains relevant wording.
“96. Indeed, they form one body, whether by hearing the word of God, or by joining in the prayers and the singing, or above all by the common offering of Sacrifice and by a common partaking at the Lord’s table. This unity is beautifully apparent from the gestures and postures observed in common by the faithful.”
This section really highlights the oneness of the Church, as set forth in New Testament passages such as 1 Corinthians 10:16-17 and John 17:11. I would think that “gestures and postures observed in common” probably refers to those prescribed in the GIRM, but there is reason to think that a culturally-recognized gesture such as hand-holding would fit in as well.
Sacrosanctum Concilium (SC), the Church’s Constitution on Sacred Liturgy, explicitly describes “norms for adapting the Liturgy to the culture and traditions of peoples,” as here:
“37. Even in the liturgy, the Church has no wish to impose a rigid uniformity in matters which do not implicate the faith or the good of the whole community; rather does she respect and foster the genius and talents of the various races and peoples. Anything in these peoples’ way of life which is not indissolubly bound up with superstition and error she studies with sympathy and, if possible, preserves intact. Sometimes in fact she admits such things into the liturgy itself, so long as they harmonize with its true and authentic spirit.”
To me, holding hands is an appropriate way for most American Catholics to relate to their coreligionists during the Mass in a culturally-recognized manner. Hand-holding is an intimate gesture, which normally Americans reserve for their loved ones. However, through our baptism, we have become brothers and sisters to each other. Hand-holding in the U.S., to me, represents a small way to make that relationship manifest.
I don’t object to people refraining from holding hands, nor will I try to hold hands in a mass where no one else is doing so (such as within the Extraordinary Form of the mass). Personally, I will continue to hold hands during the Lord’s Prayer when those around me are doing the same.