Prince Prospero gathers a thousand of his friends, "from the knights and dames of his court," to wall themselves in his castle in order to avoid the plague. These are members of the upper class, the aristocracy. The Prince has the money, the ability, and the means (the castle) to organize this event. So, at the start of the story, it appears that having a socioeconomic advantage also gives them a better chance of avoiding the plague (red death). Poe is obviously critical of this elitist and immoral attitude. He emphasizes this attitude by illustrating how thoughtless the Prince's select community are. While the masses are dying beyond their walls, they throw parties and do not have a care in the world:
The external world could take care of itself. In the meantime it was folly to grieve, or to think. The prince had provided all the appliances of pleasure. There were buffoons, there were improvisatori, there were ballet-dancers, there were musicians, there was Beauty, there was wine. All these and security were within. Without was the Red Death.
However, in the end, the Red Death does infiltrate the castle walls. To be sure, historically speaking, those with more money have always had (and continue to have) access to better facilities, health care, etc. So, to put it bluntly, it can be an advantage to be rich. And in this tale, Prospero counts on that socioeconomic advantage. But in the end, it proves futile. Poe does not challenge the notion that this has historically been the case. But perhaps he is challenging the notion that upper classes should have such an advantage. As much as this is a tale of mortality and art, it can also be interpreted as a criticism of elitism and upper class insularity.