Say you are an adoption coordinator at a shelter with 400 animals needing homes. You have a lot of kittens and cats who are in desperate need of placement. A really great family comes in, eager to adopt a kitten. They've found the perfect one, and their application is really great...except for one thing.
Their dog is not spayed.
WHAT DO YOU DO?!?
If you are the Humane Society of Southwest Missouri, you say no.
Who knew unspayed dogs and spayed kittens could INTERBREED thus contributing to the unwanted doat or kitog population.
Now if it was me? I'd ask about why the dog was not spayed. Maybe she has health problems. Maybe they do not have money to spay her. Maybe she is only 3-mos-old, and they want to wait. Maybe they are "reputable" breeders of dogs. Maybe they do not believe in removing the entire reproductive system of their dog. There are a lot of reasons not to spay a dog.
Our shelter system unfortunately reveres castration more than adoption. Or at least that is what HSSM is implying by denying an adoption based on the intact status of an unrelated species of animal.
If the dog guardians seemed interested, I would find a way to help them get their dog spayed. If they are not, then so what? All animals exiting the shelter are castrated, so even if they wanted an un-neutered male dog, it's not like he'd be getting down and dirty with the female dog at home.
To increase adoptions means letting go of outdated reasons not to adopt. Find more ways to adopt. Adopting castrated animals into responsible homes with intact animals is one way to do that. This is not unreasonable.