Would you restrict your dog/cat to come near your newborn?

I will not restrict but will keep an eye on their interaction. While pets, especially dogs, are known to be more patient and tolerant to babies, sometimes it could be an accidental tag from the baby that illicit a natural instinctual respond from the pet. In general, I think there's more good than harm to have a baby grow up with the family's furkid(s). :)