This setting is controlled by the domain administrator via the "Allow users in [domain] to publish files on the web or make them visible to the world as public or unlisted files" options that's under "Settings for Drive and Docs".
Note that after checking that option, you'll have to create a new Script in order to be able to publish it with "Anonymous" access. Existing scripts don't seem to get that option even after the setting has been changed.
Also note the Google issue tracker for this: https://issuetracker.google.com/issues/36764781