F-Droid's maintainer is against shipping builds of their app without rebranding the app id, app name and logo which is itself reasonable. However, F-Droid itself distributes builds of thousands of apps without following those same expectations for them...
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This is definitely a big issue. I did the mistake of using the same app ID for GitHub and F-Droid builds for , and the users cannot switch between two without uninstalling the other. But I guess most F-Droid users are already aware of this.
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The main issue is that users get confused when they get an error trying to install a different variant of an app in a different profile. It comes up a lot on GrapheneOS since people use profiles as isolated workspaces and can install Google Play as regular apps in a profile.
Very common for users to install an app from F-Droid in one profile and then attempt to install it from Google Play in another. It should work because the app id should be separate for each build variant with separate signing keys, but F-Droid violates that rule for most apps.