Login options for my indie game

The other option is to not deprecate, but prompt FB users to additionally do a google login (if they would like to see leaderboards).

People may be overwhelmed these days of all the Apps that want them to create an account and login every time they use those Apps, especially for games. If I install a mobile game then I don't want to register for everything or even give someone my social meda data. Maybe you are not trustful enougth to handle those data carefully, at least in those peoples minds.

The best solution would be to make the login optional unless you really need to know which user you are currently facing and if so, try getting trusted to be able to handle their data properly. The last is less coding but more community management

Why does the game need a login at all?

My order of preference would be:

1. No login.
2. Game-specific login.
3. Google login. (I don't like to give Google any more information about my personal life than necessary.)
4. Facebook login. (I don't have a Facebook login, and I'm certainly not going to create one just to play a game.)

..but the ordering of 2-4 is pretty much irrelevant, because if the game requires any login at all, I'll almost certainly uninstall it without playing.

Note that you can have unique user ids without logins.