How can "The Masque of the Red Death" be read as a political statement?

One way to look at this from a political framework is to acknowledge that Poe is making a statement about the decadence of the wealthy classes and how that decadence is a way of being in denial about death. The people attending the party at the prince's palace think they are safe from the plague that is ravaging the kingdom because they enjoy lives of luxury. There is a bit of truth inspiring the plot of the story, however.
Indeed, in medieval times in Europe, some wealthy people were somewhat safer from the plague than the lower classes because of the basic differences in living conditions. The bubonic plague was spread by fleas living on rats, and the poor were more likely to live in areas where there were rats due to poor hygiene and crowded conditions. Wealthy people also had better access to facilities for bathing and cleanliness and took to wearing pomanders, which were containers filled with essential oils and herbs, which provided some small amount of immunity and protection due to the antibiotic properties of the plants. Access to such materials was as a result of wealth and literacy, and both can be seen as political issues, since the poorer classes lacked both money and education. There was also the accompanying stigma associated with the greater prevalence of the plague in crowded living areas where the poor were disproportionately affected.
The fancy costumes and elaborately decorated chambers in the castle are a sort of commentary on the difference in lifestyles between rich and poor, as if the clean, bright colored rooms and clothes could somehow protect residents from sickness, simply by virtue of their conferring wealthy status on those present. But as the story shows, even sequestering oneself away in a castle is not a protection against this sickness, which is highly contagious and works very quickly to kill those infected. Once a visitor (dressed like classical images of the Grim Reaper, but in red) arrives, the sickness is brought to the gathering and all of those present fall ill and die: "and the Red Death held sway over all!" The story's ultimate message is that wealth and comfort are only delaying the inevitable truth that death comes for everyone eventually, regardless of social status.

Edgar Allan Poe's story "The Masque of the Red Death" can be read as a political statement. The aristocrats prior to the French Revolution tried to cloister themselves in utopian settings such as Versailles, where all was peace and plenty, harmony and happiness. Unfortunately for the nobles, the hungry masses broke in, and the Napoleonic era changed Western thinking forever. The common people never felt the same about the aristocracy again, and the aristocracy never felt so confident and secure. God was no longer on their side.
In Poe's world there is no security. Everything changes. Nothing is known for sure. Poe was a revolutionary in spirit. He was actually a contemporary of Napoleon briefly. Napoleon died at Saint Helena in 1821, and Poe was born in 1809. So Poe would have been twelve years old when Napoleon died. They were that close together in time, although it seems as if Poe was living in an entirely different era.
In "The Masque of the Red Death" there are many commoners dying outside the walls, but the focus is on what is happening to the aristocrats who are sequestered inside, trying to pretend that their lives are going on as usual. Characteristically, they care nothing about the lower classes, and they divert themselves with their traditional frivolous pleasures and consumption. Poe had once been an insider, but now he was an outsider. He shows not a grain of pity for the aristocratic ladies and gentlemen being murdered by Death. It seems likely that Poe would have had no pity for those ladies and gentlemen who suffered from the French Revolution and its Napoleonic aftermath.