"error: XDG_RUNTIME_DIR not set in the environment." when attempting to run nautilus as root

When you run software as another user you're in fact starting the new minimal and isolated environment that doesn't carry on some "excessive" variables (among others variables responsible for injecting libraries or setting certain privileges). Replace your sudo nautilus call with the following - it will carry on user-specific x server settings from the current session:

pkexec env DISPLAY=$DISPLAY XAUTHORITY=$XAUTHORITY nautilus

This is a one time low level solution but it will work on a malconfigured machine. If you want to permanently "fix your sudo" you need to find the issue with your environment configuration and correct it as described in other answers.