Any rabbit can be entered in shows, doesn't even have to be purebred, but anything not purebred and specifically bought as show quality is likely to be disqualified. The American Rabbit Breeders Association runs all shows in the USA, and they have standards which, in my opinion, are a bit more DQ-heavy than other species (I've also shown chickens, pigeons, and dogs). The rabbits have to be within a certain weight and of a standardized color (what colors are allowed varies breed by breed - some breeds, like Mini Lops, are pretty lenient and allow almost anything, some are more strict, like Giant Angora, where they come in a bunch of colors but only whites can be shown). Showing can be stressful on rabbits, and the travelling can be as well - most show rabbits are specifically bred to handle that stress well, and exposed to it and practiced with from a young age. I've been showing rabbits for a while now, and if I get a rabbit that doesn't seem to enjoy coming out and showing, I just don't show it.