Why is no one allowed either into or out of the abbey?

To put it simply, no one is allowed in or out because "The 'RED DEATH' had long devastated the country", & Prince Prospero's sole reason for bringing "a thousand hale and light-hearted friends" into his castle is to remain immune from the disease. The measures to which the prince goes to keep the illness at bay are remarkable:

A strong and lofty wall girdled it in. This wall had gates of iron. The courtiers, having entered, brought furnaces and massy hammers and welded the bolts. They resolved to leave means neither of ingress or egress to the sudden impulses of despair or of frenzy from within.

So, the wall and the welded doors assured (or so the prince thought) that no one could enter or exit the abbey. Thus, all those inside "might bid defiance to contagion." They wouldn't worry about those folk dying a horrible, bloody death outside; instead they would party. After all, they had all the entertainment they could want:

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."

So, the wealthy are safe and secure...or are they?