Alfie, a mixed-breed, demonstrates the Westminster's agility test. Associated Press

Last month came word that mixed-breed canines—mutts to you—would be part of the action, after a fashion, at the venerable pageant that's purely for purebreds, the Westminster Kennel Club Dog Show.

This weekend, before the Monday start of its 138th annual competition, Westminster will be staging an agility championship that measures skill and speed in events like the high jump, the ramp-run and the tunnel-dash, and the meet is open to canines of uncertain heritage as well as to the papered and pedigreed. In the alternate world known as the dog fancy, this is a stunning turn of events on the order of the Dom Perignon vintners participating in a taste test with the folks at Welch's grape juice.

In fact, the dog decathlon isn't the first instance of mutts at Westminster. In the show's early years, before the establishment of the American Kennel Club—the vaunted registry of purebred-dog pedigrees—entrants included Nero, a cross between a St. Bernard and a collie; Bruno, a Mastiff-Newfoundland hybrid; and an English setter-Newfoundland mix answering to Palmer.

"It was kind of a free-for-all," said David Frei, the communications director for Westminster and the show's TV co-host. Because there weren't yet any written descriptions noting the ideal appearance and characteristics of a particular canine specimen (the so-called breed standard), "we just allowed any dog to be there," Mr. Frei continued. "We really didn't have a yardstick to judge them against. It was just someone giving them the eye and deciding which one was the better dog."

For the mixed-breed division of man's best friend those were the days. But with the emergence of the AKC, which recognizes only purebreds and serves as the governing body for member clubs like Westminster, there was no longer a place in the show ring for hybrids (think cockapoos, labradoodles, etc.) even though myriad dogs welcome at Westminster have complicated family trees.

The Poodle and Irish water spaniel, for instance, may have figured in the creation of the curly coated retriever. Pointers may have a past that includes the foxhound and Greyhound, while the Cesky terrier owes a debt of thanks to the Scottish terrier and the Sealyham terrier, according to Mr. Frei.

But such tinkering, often in the name of building dogs with multiple skills—for example, the ability to hunt vermin and herd sheep—occurred generations ago. The traits, talents and temperament of the curly coated retriever and the Cesky terrier have long been set, and that's the point.

"People ask me all the time, 'Why don't you include mixed-breed dogs in the show?'" Mr. Frei said. "Well, what would we judge them against? What's going to tell us how tall this mixed-breed should be or what kind of coat it should have, what color its eyes should be or how its tail should be set?

"I see golden doodles all the time on the street," he continued, referring to the popular amalgam of poodle and retriever. "I haven't met one that didn't have the greatest personality and temperament. They are wonderful dogs. But they all look different. Some are tall and some are short. Some have this kind of coat, some have that kind. You have to be able to look at a dog and say, 'Yes, that's a golden doodle'—instead of, 'Oh, yes, I see a little of this and a little of that.'"

Such would-be contenders have had to find acceptance and trophies elsewhere. Some have done so at the Mixed Breed Dog Clubs of America (MBDCA), a registry founded in 1978 to offer members the same opportunities that the AKC provides its discrete population, for instance awards for obedience and conformation. "People wanted to be able to get titles on their dogs the way owners of purebreds have always been able to do," said Kitty Norwood, the president of MBDCA, which has 130 members.

Proof that you really can teach an old dog new tricks, in 2009 the AKC, perhaps on the scent of a new revenue stream, created the Canine Partners Program. For a one-time $35 fee, it allows dogs ineligible for AKC registration to take part in obedience, agility and other competitions alongside purebreds. So far, 226,000 dogs have been enrolled. "Owners of mixed-breed dogs wanted to participate in our events, and we listened to them and gave them what they wanted," said Lisa Peterson, the communications director for the AKC. "We have embraced mixed-breeds, all dogs."

Not everyone is feeing the love. "I think that owners of purebreds look down on mixed-breeds," said Ms. Norwood, who herself has owned a German shorthaired pointer and a Brittany, but currently has what she believes to be a Labrador-German shepherd blend. "When I've been at AKC shows, I've felt like people were saying 'eeuw.' And when mixed-breeds did place in a competition, the feeling from purebred owners was 'they took a spot from us.'

"I just want to tell people to lighten up," Ms. Norwood added. "We all go to the same veterinarians and pet stores. Why shouldn't we play together?"

Ms. Kaufman writes about culture for the Journal.