Diagnosis
The Motion feature, which uses the 13MP camera to track movement, is enabled. This is the core function of the Show 10.
How to Fix It
Disable Motion. Swipe down from the top of the screen. Tap the Settings gear. Select Camera & Privacy. Tap the toggle switch next to 'Motion' to turn it OFF. The device will no longer rotate.
If That Didn't Work
If the toggle is unresponsive, disable it via the Alexa app. Go to Devices > Echo & Alexa > select your device > Camera & Privacy > Motion, and turn it off there.
Heads Up
Disabling Motion fixes the rotation, but the camera is still technically active for video calls. To fully disable the camera lens, use the physical camera shutter slider on the top of the device. You will hear a click.