We have found that a significant number of users will just quit the app if presented with a "sign up or login" with Facebook screen at the beginning of the flow.
With this, they don't have to give us any personal data and can start using our app right away. If they want to activate social features later it is really easy to upgrade their token without having to worry about merging accounts.
Edit: regarding the user side, the problem for a lot of users isn't that they don't trust Facebook. It's that they don't trust the random app/website that is asking for their Facebook data.