Packages from the contrib repository are libre, but have non-free dependencies, so they can't be used without also using non-free software.

Using a deblobbed kernel is important, but it will not prevent the installation of other non-free software. In order to be certain that you are not using non-free software, you should use a libre distro like Trisquel or Parabola that is committed to only including free software. Debian should not have the non-free and contrib repositories which is why it is not endorsed, but because they at least make sure that the main repository only includes libre software it is usable once you disable the other repositories. Mint has a single repository that contains non-free software, so it should not be used at all. Magic Banana's comment explains the problems with Ubuntu. There is also no reason to attempt to liberate Ubuntu, as you would be repeating a task already accomplished with Trisquel.

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