Take note that God did not say there could be no changes within the family. He did not create all the varieties of dogs, cats, animals, etc. Many changes have since occured to produce a wide assortment of varieties within the family. Cats have always remained cats. Dogs are still dogs.
Men are still men.
From a good gene stock, multiple inbreeding would cause diversity without doing too much damage. Subsequent interbreeding of tainted-generations would cause problems. Mutation has only been responsible for producing a new variety of the same species, but never originating another new kind. Some are smart, others dumb. Some have short tails and some long.