This is particularly "flowery" language; that is, it is not something stated directly and instead written in an overly complicated manner to appear sophisticated or fancy.
The phrase would be understood by most native English speakers, but perhaps not children.
The word "draped" means
to cover or adorn with or as if with folds of cloth (Source)
"Draped" is therefore a word with a very critical visual component. Someone draped in rags would appear poor, while someone draped in silks would appear wealthy. What someone or something is "draped" in very much affects their appearance and can affect opinions about them.
The author says that something is draped in perception, though, which doesn't make sense literally: perception isn't a physical thing! Speaking conceptually, however, perception doesn't need to be physical. Our perception of others governs our opinions of them, whether that is the observation of their appearance, what they say, or how they act.
The author is making a metaphor that ties to the meaning of both perception and draped, and is roughly saying
What we see of performers and performances that appear on a theater stage are heavily influenced by how we perceive them.
That might sound obvious, as sight is one way that we perceive things, but perception itself is a lot broader than just sight: we have a lot of opinions and expectations that can shape what we think about what we see.
The author elaborates what they mean in one of the following sentences to confirm this:
We judge them by how they appear and how well they follow the script we expect.
A similar sentiment can be seen in the popular saying "Beauty is in the eye of the beholder," which means whether or not something is beautiful depends entirely on if we perceive it to be beautiful.