One known problem is that on Firefox for Linux, every font you install via the package manager becomes a System Font, and thus is immediately “visible” as soon as Use Document Fonts is enabled, irrespective of the setting for CSS font visibility. I’ve even asked about here if it is possible to run multiple fontservers on a single session, as that would help palliate the fingerprinting by running Firefox profiles connected to different font lists.

As a relatively useful alternative, you can have Firefox profiles on different users, each having their own fontset available at .local/share/fonts, but for that to work you also have to remove all those extra fonts you installed via the package manager.