The story pokes fun at American pragmatism and republican (anti-aristocratic) sentiments, but in doing so also satirizes the British for being stuck in the past and ruled by traditions such as fear of a ghost, which functions as a stand-in for all the fears that hold the English back and need to be buried and laid to rest.
As for the Americans, the story first satirizes the can-do attitude of the new arrivals to Canterville Hall and their practical ways of solving problems. For example, when the Canterville ghost leaves bloodstains on the library floor, the Otis family responds by scrubbing them out with Pinkerton's Champion Stain Remover. The "proper" response would be fear, but the Otises will have none of that:
"'This is all nonsense,'" cried Washington Otis, 'Pinkerton's Champion Stain Remover and Paragon Detergent will clean it up in no time!'"
Wilde also satirizes the American's lack of respect for English tradition. Rather than be fearful of the ghost that has haunted Canterville Hall for centuries, the Otises fight back. When the ghost tries to scare them by rattling his chains, Mr. Otis says:
"'I really must insist on your oiling those chains, and have brought you for that purpose a small bottle of Tammany Rising Sun Lubricator.'"
Finally, Mr. Otis is skeptical of Virginia inheriting the costly heirloom jewels of Canterville Hall, saying:
"All such vain gauds and toys ... would be completely out of place to those who have been brought up on the severe, and I believe immortal principles, of Republican simplicity."