This seems to be a case of "damned if you do; damned if you don't". Session relies on Firebase to get faster notifications from Google servers. This can be disabled in the applications preferences but changes the behavior from push-notifications to polling Session's decentralized messaging network, which makes messages notifications slower.
For the sake of clarity it would be nice if instead of making such a vague pronouncement, F-Droid would specify precisely what about the upstream source code is not entirely free.