it's not a matter of allergy ONLY. It's more like safety. Both animals and babies can be very unpredictable at times. Babies curiosity may drive them to go like ..."what would happen if I pull the cat's tale" and the cat may get aggresive towards the baby. I don't know, it's just common sense...

Having said that, I feel totally comfortable to allow my daughter to play with my dog or cat, but only if I am supervising. And that was only after my daughter was six months old. I would never let an animal near a newborn. But maybe that's just me.