I'm a developer, and I've worked with this before, but the library included here has only the purpose of analytics, and is not required for anything else.
Google has recently been moving GCM over to FCM, since the Firebase acquisition, and FCM has a hard dependency on the analytics library for some reason (even if you're not availing of the service - perhaps as a veiled upsell attempt).
It seems very likely that Firefox would be making use of GCM/FCM - I think most major apps do - so this could be it.
Incidentally, this same topics is one of the main controversies around the development of the Signal chat client - it uses GCM, which a good few prospective users object to on similar grounds.
Unfortunately, unless you've rooted your phone, GCM/FCM is the only battery-efficient way to provide push to Android phones.
> Unfortunately, unless you've rooted your phone, GCM/FCM is the only battery-efficient way to provide push to Android phones.
But, and this is the interesting part, the userspace library of FCM can be easily reversed and cloned (the information required for that is here https://gist.github.com/justjanne/153bd4886f92be0ee57fb40842...), and the system-side part of FCM has been cloned in an open way (see the µG project).
I was aware of the µG project (it requires root to install though), but I'm not sure I see the point/relevance of cloning the userspace library outside of using it with µG. If you don't have µG, your cloned userspace library is still sending everything through Google's servers right?
Note: I should possibly have been clearer above by saying "is the only battery-efficient way to provide push to Android phones without root"
IIRC, Signal now falls back to not using GCM if it isn't available on the phone, so users concerned with that which don't have Google Play Services on their phone can still use Signal. Of course of it is available Signal will use GCM, for the battery savings.