Poe primarily believed in the inevitability in life the law of of cause and effect - that nothing done could ever be escaped.
Poe delved most deeply into the human psyche, but he also was a sharp critic of society at large, and its many foibles.
The theme of "The Mask of Red Death" could be said to be a broadly social theme - that is, he paints and unflinching picture of the uncaring aspect of 'higher' society, the great gap between the entitled and poor.
Poe himself, as a forever struggling writer who's goal in life was to be a gentleman writer, successful on a large scale, had a personal axe to grind with the upper classes. In the story, Prospero (an ironic name, prosperous, given his end) takes great precautions to protect his noble abbey from any hint of intrusion or infection from the outside plague. Those precautions fall away when the guest at the masquerade, Red Death, appears, soon infecting everyone there.
Poe believed in the inevitability of a universal justice - however terribly it came - by the hand of Montresor in "A Cask of Amontillado," by the dissolution of "The House of Usher," and here, by the plague infecting all the 'special' people who thought themselves safe.
Poe ultimately believed that no one was ever safe in this world and universe from what they themselves had done.