BTW. In my case the app they urged me to replace the stock keyboard with a version that had been built without support for Norwegian. Is the language data in Android non-free?
Most apps aren’t possible to be built reproducibly, though, as the Android developer toolkit was never designed for reproducible builds and relies on stuff like filesystem ordering of files (which differs between machines).
Reproducible builds are the best option for such a store :)
They do reproducible builds starting from publicly available source. Given the AOSP design where code signatures are mandatory and updates are only allowed if signed by the same key, they're taking the best feasible approach.
F-Droid can't replace a version installed form GPlay with it's own version as they are (except a handful) signed with a different key.
It also won't even show you these versions anymore unless you enable an expert settings options.
Since then I've head that the F-Droid operators insist on signing all apps themselves, instead of the developers' signature. That's as bad as the TLS inteceptors that insist on accepting an extra CA.
Some people seem to think that F-Droid is obviously preferable to Googleplay. That is, at the very least, not obvious.