Thread is actually very dangerous for cats. A piece that is swallowed can cause life-threatening intestinal problems requiring surgery. Same with yarn. I keep all of my thread away from my cats!!! Spools of thread are especially dangerous because of the long length of thread involved.
My kitty almost died after playing with a bobbin while I was gone. She didn't eat or drink for 4 days but just sat looking at her dishes of food and water. The vet found thread wrapped around Boo's tongue with the ends swallowed. She couldn't stick our her tongue to drink or eat. After the thread was clipped and she got IV fluids she was OK. But now I am careful about threads where kitties can reach.