If you look it up on the USCCB website you’ll see it has been discouraged to hold hands during the Our Father during mass. However, people insist on doing it; even when they know this. When I taught RCIA and CCD I tried to teach the students and catechumen/candidates on this, but I was overrided with this comment “We’ve always done it and we will always do it”. Even though many of us want to be obedient to the Vatican’s wishes, there are many who do what they want. I put my hands together in prayer and usually no one tries to grab my hand.
In addition, a priest I met while in Korea told us that it is a distractor for him when people jump out of their pews to hold hands and if nothing else consider that movement out in the pews when it is loud and busy is distracting. Another distractor is the raising and lowering of the kneelers, this could be done alot quieter, slamming them down is unnecessary. In the military you never heard kneelers being raised or lowered. He was a phenomenal priest, he held no punches but I had so much respect for him.
Also, when we extend the sign of peace to others, I would like to ask for everyone to consider that some of us, love to show our expression of love, but some of us elderly have arthritis and it is extremely painful when some young whipper snappers put a bear hold on our hands and just crush our joints. It is painful. So, if someone just waves and is reluctant to shake your hand, don’t take it personally, for me it’s a matter of protecting my hands from being squeezed and causing pain for the rest of the day. I know no one does this intentionally, so I’m just saying… please be considerate and don’t take it personally.