I gave a talk at Google I/O 2016 called “Recipes for App Development with Firebase” about ways that you could make use of Firebase in two different kinds of apps, including a ride sharing app.
Firebase probably doesn’t offer every single tool and component required to make an app like that successful (such as payment processing), but it could provide a foundation to get started.
Yes, you can use Firebase or other BaaS - Backend as a Service platform to create an Uber like backend. Please read the article below to understand the pros and cons of Firebase.
Firebase x Parse Server
Question needs more depth. Why do you ask this in the first place? Do you see any problems using Firebase for this? Or just asking for opinions?
Like anything else, at one point you’ll write your own back-end for your app. For an MVP, it’s probably more than enough.