Dogs have come a long way. Their evolution from wolves took centuries, whereas today they can be made to look like robots, kangaroos, crustaceans and mermaids by extreme animal groomers in one sitting. It’s not just dogs—around the world chicks and rabbits are dyed Crayola-bright in time for Easter, and cats’ fur is buzzed to resemble flowers.

The artistry is laudable, but the ethics are questionable. Animal rights charities argue that pets are being anthropomorphized in unsettling new ways: People see them as an alternative to children and, without new shoes and school books to buy, there’s cash available for multicolored makeovers. Some animal lovers worry that in addition to experiencing physical discomfort, pets are also being humiliated. “We are not greatly in favor of d...