Your screenshot does not really show anything other than the fact that Ally attempts a connection to Facebook (it's not even clear how it was blocked). You can see the amount of people telling you to unblock NTP, which you stated isn't blocked - that's a clear sign that you haven't presented you data in an easy to review format.
Why not show what exactly is blocked by the firewall, how the rules are configured, and disabling which rule exactly gets the app to work? E.g., if you block Facebook by redirecting to your own HTTP server that responds, the app may decide to bork because of a failed certificate validation - resolve the Facebook domain as NXDOMAIN in your DNS, and see if that helps.
The fact that they use Facebook APIs is infuriating, regardless.