All breeds of dog were created from existing stock to do something in particular. Just because we tend to keep them all as pets in post-modern times doesn't mean dogs have lived and worked with human beings for centuries. The dachshund was designed for one thing: going to ground. Whether that means hunting badgers, rabbits or whatever, it's what they do.
To begin to breed the dachshund for a purpose other than going underground after things that could shred it is contrary to the mission of the Dachshund Club of America, as well as dachshund clubs all around the world. Generally the fear of dog racing has turned what was once a humorous demonstration-only trial for amusement at Dachshund Club of America sponsored events into something not so humorous.
However, as racetracks have begun having wiener dogs races and even wiener dog racing days, it is feared that a dog not meant for racing will begin to be bred for speed. Partly their objection is to the corruption of six noble breeds of dog, but more than that, they are concerned with the fate of racing dogs and most especially when they could be dachshund.
Anyone who has ever owned a dachshund knows how smart they are and how poorly they do in confinement. Imagine how badly behaved and very unhappy those dogs would be compared to the greyhound - a dog that is a bit less cerebral and patiently resigned to their fate far easier than the feisty and dangerously clever dachshund.
As an organization dedicated to the preservation and welfare of the breed, the Dachshund Club of America has repented their wiener dog racing ways and are asking people to do the same, no matter how funny it is.
Conversely, the Dachshund Club of America encourages dachshunds to participate in American Kennel Club earth dog trials, as terriers have for a very long time. They are, of course, naturals at this activity that involves a set number of turns in an underground maze of sorts, with a cage of rats as the ultimate goal.
Dachshunds are incredibly good at hunting down vermin and other well scented objects, so they naturally excel at it. Because they're so well designed for such a task, they are excluded from the American Working Terrier Association trials.
Any breeding done to encourage this trait or this sport, which is unusual in that its non-competitive and dogs that have been altered are allowed to compete. The only stipulation is that a dog must master one type of course before moving on the other one.
This is called earning their "legs" as they must get four passing judgements on AKC courses before moving on to the next class. Though all types of dogs are allowed, many champion dogs are also master-level Earth dogs.