F-Droid is just another walled garden. You may like the walls but they are walls none the less.
Discussion
I call bullshit. You don't even need an user account to use #fdroid and can even add your own 3rd party repositories to any decent #fdroid client.
They say it themselves “On this site you’ll find a repository of FOSS apps”. Your app must be FOSS to be listed on their Store.
They will ban apps for other reasons besides not being free software.