macOS protects your privacy and will display a prompt to ask if Sketch is allowed to record your screen the first time you use the eyedropper tool. The app needs permission to record your screen to sample colors when using the color picker and does not record your screen for any other purpose. You can change these settings by opening System Preferences on your Mac and navigate to Security & Privacy > Privacy > Screen Recording.
To ensure apps on macOS cannot invade your privacy, they are not allowed to “see” anything but themselves. Applications without permission to record the screen will see the desktop wallpaper instead of the actual screen contents.
Using the eyedropper tool in Sketch will work without permission to record your screen. However, if you wish to use this tool to pick colors from other applications, such as from a website displayed in Safari, Sketch needs permission to “see” your screen.