[ysavir]

The relevant context is the context in which it existed--that of a Roman library in pre-Christian Rome, making it a Roman library with no context of paganism. If it were a collection specifically of pagan writings assembled and maintained after Rome's widespread conversion to Christianity, then the pagan aspect would be meaningful, as it describes the relevance of that library to the society in which it existed.

To call it a "pagan" library now fails to describe it in the context of what it was at the time as well as what it is today, and instead is needlessly and aimlessly anchoring the perspective to the Christian world. It would be as if I described the library as being a Goy library--sure, I can, and wouldn't be technically wrong, but it's a meaningless distinction, and one that's more concerned about expressing the speaker's context than the subject's context, and the speaker is not relevant.

[tourmalinetaco]

It’s not a meaningless distinction, as it cements it rather firmly in a broad era within a specific context of thought, unlike referring to it as a Goy library. If you refer to it as a Goy library, that both brings it within a Judeo-Christian context and completely loses all meaning. However referring to it as Pagan you now are more informed of the era and schools of thought employed at the time.