Handling babies from the day they are born is very important. Counting the babies, checking them over for injury and cleaning out the nest to remove any uneaten placentas or dead babies should be done as soon after birth as possible. If the nest is not inspected, then placentas or dead babies will start to rot and will kill the babies.
The mothers instincts to care for her young is stronger than any strange scent on her babies. I try to wash my hands before handling babies, but other than that I take no other precautions. I have worked with many foster rabbits with babies, and they will meet me the same day I start handling and checking the babies. All of them have continued to feed and care for their babies regardless of me handling the babies.
Not handling babies I think was started to keep people from disturbing wild rabbit nests. A lot of people will find a wild rabbit nest, not see the mother around and assume it is abandoned and that the babies need to be rescued. So by telling people not to touch the nest or the mother won't come back or that she will harm the babies will keep people from disturbing too many wild rabbit nests. And in the case of wild rabbits, leaving the nest is the best thing to do, but again if the nest does get disturbed and the babies are touched, mom will still come back and care for her babies.
-Dawn