How do I turn notifications for stories on or off on Facebook?

While you can't turn off Facebook notifications for stories entirely, you can:
Notifications for Stories on Facebook
Notifications about stories follow your other notification settings on Facebook. For example, if your notifications for Close Friend activity are turned on, you'll get notifications about stories from people on your Close Friends list.
Learn how to adjust your Facebook notification settings.
Notifications for Stories in Messenger
You can turn your Messenger notifications for stories on or off in the Messenger app. Learn more about managing your stories notifications in Messenger.