There's two kinds of networking I will eventually need:
The first is the communication between the players' game clients and the game server(s) actually running the game simulation. Firebase does not provide anything particularly useful for realtime messaging, which is needed in Shmup 99 because the players have continuous interaction with each other. Firebase might be suitable for games that don't require realtime communication, but I don't know for sure and can't give any Firebase advice, as I haven't used it. For game communication I currently use yojimbo, which I linked earlier. I'm satisfied with how that is set up.
The other kind of networking I will need is between game servers or players and centralized servers for authentication, stats tracking, etc.. Firebase might be more useful here than game communication, but I won't use it because it's proprietary. I have not started working on this portion of the game, but the central servers will probably expose a web API and use some SQL-based database system. There are lots of existing libraries/frameworks for that kind of thing and I have not made any concrete choice on what I will use. Firebase provides a database system and push notifications, which may be useful if you decide to use Firebase for your persistence stuff.