I really don't care if it is a pure breed or a mutt. The temperament of the dog should gel with ours and the other dog we have. I am with you on this, that there are so many dogs out there that need shelter.. we could do very well to give a unloved dog a loving home.
Mine is not a pure breed, she is a mix of a Pomeranian and a poodle.. but looks more like a Pom. I have had other dogs that I had adopted from animal shelters.. and they were fine.. I would of course try to get familiar with a dog I want to adopt from the shelter.. I would study its habit and temperament before bringing it home.. of course getting a thorough medical examination and all the vaccinations is important too when you have another dog at home.. It would be a mutt for me..