Who is the company taking care of? Dogs or Humans? From all my unfortunate experience having to put up with my immediate neighbor's dogs, dogs in my neighborhood, and dogs at work, I've noticed a certain percentage of dog owners are the dog equivalent of a "crazy cat lady". They think "dogs are people", should have access to every place humans do, should bark all they want, and usually value a dog's happiness over the happiness of real human beings.
Also, let the inter-species pet wars begin ... right in the darn office. I'll get the popcorn.
Some people have rats as pets and carry them around. I fail to see the problem with that.
Presumably at the interview it's pretty obvious what's going on, and people ought to be fairly self-filtering about this. Diversity is good, right? You ought to be matching the company to your needs anyhow.
Plus animals aren't like humans, they don't use the restroom when they have to relieve themselves. They beg for food, stare at you when you are eating, make noises and smell.
EDIT: Just to clarify, I am not allergic to dogs and yes, I don't like pets, but I also don't mind having dog or a cat around when sitting in friends house. But, I just don't feel safe in a presence of dogs, and there's no way I would be able to do anything useful the whole day except watching over my shoulders to make sure the beast is not somewhere near me. Whoever wants to impose that kind of feelings to me is making me bad, regardless of his intentions.