When this screen appears on Logic startup, click "Quit". Then in Logic Pro X go to: Logic Pro X > Preferences > Plug-in Manager.
To deactivate the plugin: In Plug-in Manager locate "Process Audio" under "Manufacturers" (lower left side of the window) > click on "Process Audio" to display the installed plugins from this developer > untick the "Use" field to the right of "Sugar".
If activation window keeps opening, you can remove both the plugin and its iLok license management system from your Mac. The easiest way is to remove the plugin itself. Go to:
Macintosh HD > Library > Audio > Plug-Ins folder and delete the "Sugar" plugin from "Components", "VST" and "VST3" folders. Be careful not to delete plugins that you actually use.
The "iLok" application might reside in your /Applications folder. Trash the application file. Empty the Trash afterwards and reboot the Mac. Be careful though, if you use any other plugins which require iLok, then you must leave iLok app alone.