Just ask your sister is she supports people dumping unwanted cats and dogs into the wild. Cats and dogs do survive as "wild" populations, albeit in the domestic form of the species, in certain areas. Pariah dogs come to mind...
Tell her that just because she cannot love ALL animals equally, is no reason to not take proper care of pets. She's the hypocrite, because if she loved the pets, she would advocate taking proper care of them, not dumping to die a slow death.