No touching - the parents have been told to make sure people have washed their hands before touching her baby. Most posters seem to understand the reason for this.
No lifting - they don't want people to pick up her baby without their permission and, again, most posters seem to be saying that they wouldn't do this anyway.
No kissing - they have been told that people kissing newborns can be life-threatening. Not an unreasonable request.
The issue seems to be the sign, rather than the requests on the sign. I would question what it is about the family dynamics that means these parents feel it's necessary to use a sign to stop people doing things to their baby that most people wouldn't do anyway.
I agree with the poster that said someone should ask the mother if she's OK. Maybe, like many expectant MNers, she's been told throughout her pregnancy that her baby is for everyone to enjoy or she's already under pressure to leave the baby for sleepovers with DGPs.
There will be a reason for this, whether it's boundaries around pushy family members, fragile mental health or warnings from over-zealous health professionals, so it would be best to offer support and reassurance to these parents, making it clear that their boundaries are reasonable and will be respected so they feel more relaxed about visiting with the baby in the future.