This is going to be fairly a controversial topic, so fasten your seatbelts. I know this isn’t everyone’s opinion, but I’ve been doing a lot of thinking and research about it and feel strongly enough to finally step out of the shadows to speak my mind.
I don’t think we should hold hands during the Our Father. If you try to hold my hand, I won’t take yours. It doesn’t feel right to me (similarly to clapping in Mass for anything other than celebrating reception of a Sacrament). That is a time for me to be praying to God and I want to focus on my devotion to Him rather than holding someone’s hand and it becoming a distraction. My view is that it is not “proper posture” for Mass. Proper posture for the recitation of the Our Father in Mass is to fold your hands in front of you. Not to hold hands with your neighbor. Nor to hold out your hands like the priest, which is called the “orans” posture (unless the country has allowed this — more on this a couple paragraphs down).