At the simplest level, Firebase is just an online database you can use to store and get information.
For a MUD type game, you might not even need to use the multiplayer plugin if you are using Firebase, depending on your setup. Basically each player will upload their own information and request data from the Firebase server as needed, thus getting information on all the other player states.
Otherwise, utilizing the multiplayer plugin, you would probably have a dedicated host which all peers connect to that handles all information. Then you wouldn't need Firebase...
To proceed with Firebase, you'll want to answer the questions: What does each peer need to know about other peers, and when do they need it? What information needs to be saved? Then its just a matter of syncing the relevant information to Firebase.
Generally speaking, if you can organize it properly, keeping all information that needs saving in an array would allow for a relatively simple import/export system via Save and Load Array as JSON (which is simply a standard format for saving certain types of information).