The general answer is that cats normally show little interest in new babies. Either that or cats find babies off-putting because babies are unpredictable and noisy. Cats can be spooked by all the crying. Perhaps, that should be the overriding principle combined with caution.
The answer to the question in the title comes from the comments of mothers on the mumsnet.com forum and babycenter.com as I am singularly unqualified to answer it! However, I believe it is a question worth addressing on PoC.
Cats might like to sleep in baby’s cot. There needs to be supervision. Baby and cat should not be left alone together. This last bit of advice from mothers of young babies who have kept cats is probably the most commonplace and important that they provide.
As I understand it, it is recommended that a mother sleeps in the same room as her baby for the first 6 months. At night the consensus is to keep the bedroom door shut to keep the cat out.
I am sure that some mothers keep the door open at night but my reading of the situation is that, in general, a mother insists on supervising when cat and child are together and therefore when mother is asleep cat and child are kept apart.
Cat nets (cot bed cat net to protect babies when in the cot) appear to be almost universally rejected by mothers. I find this strange as it would solve the nighttime issues. Also one of mother’s fears is her cat becoming fond of the new crib/cot. When it is is bought and placed in baby’s room before baby is born the family cat may well take a liking to it and settle down in it as if it was made for them.
Mothers don’t like to see that because they foresee their cat doing the same thing when the crib is occupied by the new baby. The answer is to use a cot tent or keep the door to the room closed. Some mums put tin foil in the cot to make uncomfortable for their cat. Other deterrents are: double sided tape, or “scat mats”. Some moms realize that a cat will normally not go near the cot when the baby is in it. The problem is perhaps not a real one but but imagined.
Mothers tended to shoo cats out of cots if they decide to sleep in them in. Mothers want to “train” their cat to not go near baby’s coat. This entails negative reinforcement (harsh words used) which is not ideal.
Modern mothers tend to understand that the cat suffocating a baby stories or cats “taking the baby’s breath” are old wives’ tale. Generally, they ignore them. It is an underlying fear though.
If a cat had a habit of sleeping on the bed with the cat’s owner (the baby’s mother) this was stopped sometimes well before the baby was born to allow the cat to get used to not sleeping on the bed. The reason: to keep the cat out of the bedroom where mother and baby sleep.
The cat is probably in more danger from a child once the child reaches a certain age. Supervision is required to protect cat as well as child. Where possible very young children should be taught how to handle a cat.