Watching thread... Our rabbit loves books. We successfully thwarted him with books by gEtting baskets in the bottom shelves. May have to do the same with the vinyl.
My cat used to lick certain albums. This is something to be worried about, actually... if it's certain albums, they may be attracted by the scent of certain chemicals on the sleeves and that could be toxic. Maybe some plastic storage sleeves would be an idea? My cat hated those things.
I don't know of any way to stop it besides making sure everything is put away. They seem to be too tough for him to actually eat because the corners will have massive bite marks but not actually ripped off. He has only ruined one actual record thankfully, but now I know!