I'm guessing it might be like them having babies. I'm pretty sure townies can only have babies if the house they live in has a cot, so maybe they can only adopt a pet if they have the right items (bedding, food bowls) in their house.
Nope, when the family in question is not the active household, the furniture is largely irrelevant. When they're inside, the furniture is not actually being used so it has no bearing at all on whether or not a Sim will become pregnant or adopt a child. However, families can move to larger houses with more beds once the babies become children, but it's not uncommon to visit a house where one Sim will end up sleeping on a sofa when he/she becomes tired due to a lack of beds.
But pets are completely different in the fact that they don't actually
require pet items to satisfy their needs. They can sleep on the floor or furniture, they can use the bathroom anywhere, and can even be fed without a pet food bowl by making "gourmet pet food" from the fridge. So while I have yet to play in an pre-Pets town since I got the expansion, my guess is that the game will fill the townie homes with pets and continue from there.