Cave spinner webs are treated as solid terrain, which does mean that most movement effects can't go through them, just like they can't go through walls.
Levitation letting you go through the webs is actually not intended, thanks for letting me know about that inconsistency, I'll look into it.
EDIT: Ah, I see what's happening. The web effect is actually processing correctly, but levitating makes you immune to the rooted debuff. Perhaps at some point a 'webbed' debuff might be more appropriate here, but this is technically intended for now.