The interaction is genuine. The they have lost everything due to the feud. In addition to losing their children, they have lost other family members (Tybalt and Lady Montague. There is nothing else for them.
It is not "genuine" as the fact that the two lovers are dead is the fact and cannot be changed so whatever "good" you do can't change anything. If they were "genuine" about it, they won't have to wait until the tragic death of the two lovers to take action. I think they were only trying to correct the mistakes that they have done and rid away any guilty conscience stored in their heart
Though the reconciliation seems genuine, I must wonder if it is possible. In the end Montague pledges to erect a golden statue of Juliet. Instantly, Capulet agrees to do the same for Romeo. Are they competing once again, or is this move sincere? Perhaps falling out of the years-long feud is not so easy.
Considering the fact that the family ends when Old Montague and Old Capulet die, it doesn't really matter. I would think that it was genuine, since they "supposedly" realize the idiocy of the fued in the first place, and it killed their only children (and at the women's ages, I don't think that it was possible to concieve others) ending the family line. So even if it wasn't genuine, it would die out with the last of the Mon. and Cap.