You can not show wethers but in county fairs, jackpot, and state shows. They do not have to be registerd and the Boer goat associations will not register a wether.
In pygmy goats wethers are registerable and showable. Since pygmy goats are a pet type of goat the wethers while not really useful for anything else make great pets and show animals for young kids. They are judged on their conformation but also have 25% of the score just for their behavior and attitude to show of their "pet like" qualities. In pygmies it does make a difference if they are registered or not and can effect the price of the wether.