for pet rabbits, I know a lot of breeders actually recommend daily handling. If you are breeding for show/meat, a lot of breeders weigh the kits every day to check growth progress. I think that the don't handle rule is an old wives' tale. I think it developed because most people don't realize how little time a mother rabbit spends in the nest. They actually only feed the babies a couple times a day and only for a couple minutes. Otherwise, they stay away from the nest so as to not attract predators.
Wild rabbits might abandon babies, just from a fear of human scent, but that is probably pretty rare. Usually, though, she will just move the babies to a new nest if she thinks there is a danger.
A domestic rabbit that is used to being handled won't eat her babies just because they are handled. Twilight doesn't mind them being handled. Sometimes she watches, but most of the time she just looks to see if I brought a treat.