It is interesting that in such an environment of "infinite decorum" and "masquerade license" that any figure manages to evoke such responses of "terror, of horror, and of disgust." Yet we are told that the figure had "out-Heroded Herod" in his appearance, going beyond the bounds of what is acceptable and showing that it is always possible to offend everyone if you know how.
Let us consider how this guest is described:
The figure was tall and gaunt, and shrouded from head to foot in the habiliments of the grave. The mask which concealed the visage was made so nearly to resemble the countenance of a stiffened corpse that the closest scrutiny must have had difficulty in detecting the cheat. And yet all this might have been endured, if not approved, by the mad revellers around. But the mummer had gone so far as to assume the type of the Red Death. His vesture was dabbled in blood--and his broad brow, with all the features of the face, was besprinkled with the scarlet horror.
What is so shocking and incredible about the appearance of the stranger is therefore his choice of disguise. As it says, the resemblance to a corpse would have been approved of by the assembled masses, but what is unforgivable is the way that the masked guest has deliberately disguised himself as a corpse that has been killed by the Red Death. To have such a reminder of what Prospero and the others have fled from and also to frighten them with what their future possibly holds for them is beyond the realms of acceptable social behaviour, which explains why Prospero is quick to react in the way that he does.