For those of you who do this with something thinner than a piece of paper (like a sticky note), you’re in the clear. While Apple does not recommend using adhesive to attach said paper covering — although seriously, how else are you supposed to do it? — it is safe to leave this type of cover on when closing your laptop.
The trouble is thicker, pre-made plastic camera covers, which you can easily buy online. According to a support document recently published on Apple’s website, closing a laptop with a plastic camera cover can result in damage to the display “because the clearance between the display and keyboard is designed to very tight tolerances.” There is apparently no room for anything thicker than 0.1 mm.
If you insist on using one of these camera covers, Apple recommends removing it before closing your laptop. The company also states that the green light next to the camera will turn on whenever the camera is in use, and “is engineered so that it can’t activate without the camera indicator light also turning on.”