F-Droid is a FOSS App Store available for Android, and has hosted our apps in the past. Should get the app on it at some point.
This is going to be fairly difficult since they apparently no longer accept build processes that require remote repositories. Since the Android app uses both Maven Central and our own remote repo (and there is no intention of changing that anytime soon), this is going to be a fairly difficult task.
I think for now people without access to the play store should just get the APKs from releases.wikimedia.org. Leaving this bug open to see if things change.
Version: Android (alpha)