That absolutely IS an old wive's tale. People perhaps wanted some explanation for SIDS (Sudden Infant Death Syndrome) or "crib death" and would blame it on the cat, not on their smoking or use of fluffy pillows in the crib that would smother the baby. The habit some people have of having their infant sleep in the adult bed with them has also resulted in many infant deaths from suffocation or crushing.
I have had cats who were very sensitive and would do extraordinary things with or for their humans. One of my cats, a rescue who was terrified of most everything and hid much of the time, used to come up to the table and jump on a chair when it was time for the family to say grace. She would avoid groups of people always except that she would come to a prayer meeting held every month in my home and sit near a particular person; and she would jump up to sit next to me when I studied the Bible and sometimes put her paw on the pages.
My mother, never one for superstition or fearful folklore, would not allow us to have a cat in the house until there were no more infants around. It seemed to be common knowledge that they were baby killers.
Oh that’s a crock of hooey. A cat who was even halfassedly cared for wouldn’t have the slightest interest in what you’re hinting at, and if you starve your cat to the point that it is, I question how much you care about the kid too.
The story about sucking out the breath most likely comes from an overly affectionate cat, if anything. One of our four will snuggle right up against your face and it’s very common to wake up with a mouth and nose full of fur. Mildly ticklish and annoying as an adult, but a baby can’t push a cat who does that away, and their airway is much more easily blocked.