Okay, since I asked a few threads ago, I went ahead and checked. You currently can't skip:
>Shackling Prison
>Paperfold Academy
>any character quest not included in the main story (it let me skip Sunday's, but not DHIL's)
So if you're like me and are sitting on all the Luofu quests because lol chinaslop just know you still have to read them. This was probably stated in the update but since you can skip events now I figured I'd clarify.