Earlier quoted context omitted.
Fdroid maintainers require shipped apk's to have 0 non-free components. The only way to ensure that is to build the apps themselves (so that they can verify code and control dependencies). This means that they can only use their own keys.
No it doesn't. They could check the developer's signature against an APK built from source. It's not that difficult. 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).