I am very fortunate to have some wonderful cats that don't look at yarn as a plaything. I have heard many a horror story from friends whose cats got into their Stash, and they have come home to find a tangled mess of some of their best yarns.
The most my cats ever do with yarn related things is to swat at my drop-spindle as it's moving towards the floor. However, I've quickly stopped them from doing *that* with a gentle nudge / kick with my foot*
My cats, however, do like fabric. Anytime I lay out fabric in order to sew, they are inevitably right on top of it looking at me with innocent eyes. They do the same anytime I am looking at any piece of paper on the desk or table. Luckily, they have learned to sit quietly in the corner (after I pet them vigourously) so that I can cut my fabric in relative peace and quiet.
The most any of them do is play with my measuring tape because it's very long and has a tendency to slide around.
But, my cats are older (14+ years) so they might be beyond kitten antics of playing (and disemboweling) with a skein of yarn. So, I guess if and when we ever get a new kitten, I might have to seriously start locking up my projects and my Stash in rubber bins to prevent them from making a gnarled mess.
*I'd never ever kick a cat on purpose**, but a gentle "nip" with my foot keeps them away from the drop spindle.
**I have accidently kicked a cat, because they got very much underfoot just as I was moving my foot forward.