I do not believe in supporting designer dog breeders, backyard breeders or puppy millers. As far as rescues, yes they have a strict adoption policy but you have to remember why or how the dogs are in the rescue/foster homes. Most of their dogs they rescue have been subjected to some form of abuse or neglect and they are trying ensure the dog a happy, safe life and a forever home.
Impulse buying is a huge problem with the increase in our dogs in shelters and rescues. Again, this is a good reason some of the more reputable rescue groups will do a home visit. Before re-homing the dogs, these volunteers want to make sure that this is going to be a good fit for the dog and the new family.
For every puppy purchased from a backyard breeder, pet store or puppy miller, the buyer(s) is encouraging these people to breed again and again. It's amazing how many people when they get their "purebred" puppy decide not to spay or neuter their dog and have it in their mind to have just one litter to pay for their dog's original cost or my dog's personality is so great, just one litter or oops - my dog got pregnant by accident and it just so happened to be the same breed of dog.
I think that mutts are just fine, as long as that's why they are but I am a big advocator of spaying and neutering. Also, if one is looking for one particular breed, rescue or a reputable breeder that does all the health testing (not just "vet checked") and breeds for the improvement and betterment of the breed are the way to go.