I don’t think you’re a snob either, op. I’ve not read As You Like It, but certainly know who wrote it. As a pp said, this isn’t about having read the thing, it’s just general knowledge.
The shocking thing is not what individuals don’t know, it’s how little we value knowledge as a society. There have been threads on here where other ops have been shot down for such crimes of snobbery as being unhappy a primary school teacher didn’t understand basic concepts about fractions or questioning a plan to relax English standards for universities (how can they be relaxed any more, I’m sure many of us are thinking).
Time and again these things are held up as advanced skills that only a specialist would be expected to know. Why should a science graduate be expected to know how to use paragraphs? They aren’t doing a PhD in English, etc. It’s depressing.
I don’t think I’m a snob because I apply this to myself too. I studied English at university, but was hazy on many points of punctuation until I bought myself a book several years after graduating because I wanted to be better. There are still things I’m sure I’m ignorant of. Likewise, whole swathes of history not taught in school.
This is the anti-elitist, anti-intellectual culture where the very worst thing you can be is a ‘snob’ and people should be left to their ignorance (even if it’s not what they would choose). You can see the results over on some of the coronavirus threads.