I think it depends on how comfortable you are leaving your things. CC may be Disney, but it's still a beach with lots of people. I don't recall any reports of theft, but that doesn't mean it doesn't happen.
Anyway, we don't usually bring anything but sunscreen, snorkel gear and towels in a bag at CC. We try to find chairs close to where we want to be, and would go back and forth occasionally to check on our stuff. But most of the time, I can see it from the water. When my husband wants to take some photos, he would bring the camera, take the photos and when he's ready to go into the water, he brings the camera back to our stateroom. I know it's a bit of a hassle, but he doesn't seem to mind.
The only time we needed to stay with our stuff was when, as part of our excursion, we had a little bit of time at the beach in Cozumel. We brought our camera and I did stay with our stuff while the rest of my family went snorkelling. No issue since I don't like snorkelling anyways.