I would like to know if cat hair is unhealthy for a newborn baby. My son and daughter- in- law have a cat they took in as a kitten. The cat is now a year old. They are very attached to this cat. He is a very sweet cat . But he looks to jump into the baby s basinet.He is always climbing on the countertops and what concerns me is his coming from the litterbox onto the countertops. They also allow him on their bed .My son is holding the baby with the cat a couple of feet away from them. Is it true that it helps the baby s immune system. I m I being too concerned about this. Thank you -First time Grandma