If you are owned by a cat or cats, as am I, your first thought is of your cat getting some messy baby germs!
We own a cat — actually, he owns my husband — but I am particular about germs getting on the grandbabies.
Our cat actually wound up napping with the visiting 2-year-old recently, and I did not freak. But I would not be happy about having someone else’s cat near an infant in my care.