Apple says that the clearance between the display and the keyboard is designed to very tight tolerances, which can be problematic. Covering the camera can also cause issues with automatic brightness and True Tone.
If you close your Mac notebook with a camera cover installed, you might damage your display because the clearance between the display and keyboard is designed to very tight tolerances. Covering the built-in camera might also interfere with the ambient light sensor and prevent features like automatic brightness and True Tone from working. As an alternative to a camera cover, use the camera indicator light to determine if your camera is active, and decide which apps can use your camera in System Preferences.
The warnings from Apple likely stem from complaints from MacBook Pro owners who have seen their displays crack after covering the camera, and there are multiple reports and warnings on sites that include MacRumors and Reddit. The issue appears to be especially bad with the new 16-inch MacBook Pro models that have thinner bezels.