You can turn people down as long as your decision is not based on gender, race, religion, age, ethnic group, etc.
You can turn them down for other reasons as long as you use the same set of criteria for everyone, such as fenced yard, no apartment dwellers, young children etc. But you must use the same set of criteria for everyone.
As a private citizen I believe you can sell or not sell to whomever you please. Commercial retailers don't have that privilege.
Also housing is a basic necessity, having a dog is not.

Isn't it sad that we have to start our posts with disclaimers, to keep from getting jumped on.

I might just add a disclaimer to my signature. LOL