I have a picture of people holding hands during the Our Father, from 1965.
The first edition of the GIRM was 11/18/1969; revised 3/26/1970; and emended 8/15/1972.
The second edition of the GIRM was 3/27/1975; emended 1/25/1983.
The third edition of the GIRM, study edition was released 7/2000 and the third edition of the Roman Missal in 3/2002.
Rome has undoubtedly known about holding hands during the Our Father since somewhere at or during the first edition; and none of the editions have addressed the matter, although there have been a steady stream of complaints about it since it’s inception.
At least as long ago as 1995, the USCCB petitioned Rome to allow the orans position during the Our Father and to restrict (as in, eliminate) holding hands, as part of some changes being proposed in the ICEL Sacramentary. The proposals were sent to Rome; Rome replaced the new Roman Missal, and subsequently officially rejected the changes requested by the ICEL Sacramentary proposal after the Roman Missal was released.
Nothing was said, either about the holding hands, or the orans position, by Rome in the Missal, nor has there been any directive from Rome concerning the postures (and there have been other documents from Rome concerning abuses in Mass).
The short of it is that Rome has been aware for decades of both the posture of holding hands during the Our Father, and of the orans position during the same, and in repeated releases has chosen to ignore the matter. Not outlaw it, not set a posture to be held; simply ignore it.
Anything to the contrary is personal opinion and holds as much weight as any other personal opinion.
And as to what I do, I follow the suggestion of Archbishop Chaput, which is that all sides need to act in charity; meaning, if the person next to me wants to hold hands, I do so, and if they do not want to hold hands, I do not do so. I simply don’t have a dog in this one, and it does not create an emotional issue for me. I don’t care if we hold hands, or don’t do so; and if Rome institutes a rule on the matter, I don’t care which way they rule; I will abide by it.