I would tend to think that babies immune systems are developed more quickly when exposed to pets, whether it be due to micro-organisms present or other factors. Certainly breastfeeding is an important boost to childrens immune systems but I think that the pets may also be a contributing factor.
Homes without pets tend to be more sterile environments generaly and it is my opinon that children raised in more sterile environments will have a lower immune response when exposed later. That does not mean that I condone children being raised in filthy surrondings, just that it is possible that being over zealous about cleanliness can actualy contribute to health problems