I wrote this article and accompanying sample while contracting at Microsoft. It takes the basic Azure Easy Tables implementation of a leaderboard from the first sample I wrote, and adds Facebook Authentication.
This was more work than I expected, because of numerous compatibility issues I uncovered as I worked. For example, the Facebook SDK for Unity did not work with the newer Unity 4.x scripting upgrade, but the Azure Mobile Apps SDK that I used previously to connect Unity to Azure required .NET 4.x.
In the end, I wrote some Azure serverless functions that served as the middle-man between my Unity project and Azure Mobile App. The sample uses the Unity Facebook SDK to authenticate with Facebook and pass along the authentication and leaderboard data to the Azure functions via UnityWebRequests.
It worked, but I would say the experience exposed some serious usability concerns with using Azure, Facebook, and Unity. Shortly after / during this work, Microsoft purchased Playfab, which I’m sure has changed the way they plan to approach the problem.