> No, they aren't. Not in any way, shape, or form. Private companies don't have any obligation to continue showing anything. They don't have any such 'moral' obligations at all. They aren't going into libraries and purging books.
What if the libraries are privatized?
> An actual purge would be something like systemically recalling, redacting, and deleting any remaining records of art that involve Cosby. Saying this is 'our libraries being purged' is completely alarmist and untrue.
No. An actual purge would consist of removing the work from circulation and locking the remaining copies in a restricted section in the library (a giftschrank). What you describe sounds like it's inspired by the fictional total censorship regime shown in 1984 [1] than by nonfictional examples.
[1] Which was probably lie even in the context of that fictional world; I wouldn't be surprised if the Inner Party actually had accurate archives kept in a giftschrank.