Firefox users who prefer to download the browser without the unique identifier may do so in the following two ways:

  Download the Firefox installer from Mozilla's HTTPS repository (formerly the FTP repository).
  Download Firefox from third-party download sites that host the installer, e.g., from Softonic.
It's nuts and another indication Mozilla doesn't understand the reason they exist, but it's not that hard to get around... if you're one of the 0.1% that hears about this.

3) Install Firefox from your operating system's repository instead of from Mozilla

These builds still have distribution-specific in-built API keys for some of the built-in services such as Google Safebrowsing, Google Location Services and Mozilla Location Services. See [1], [2], [3], [4], [5] and [6] for details and examples.

Additionally, upon first launch of Firefox, a unique client identifier is created, and this is sent to Mozilla by default probably before you get a chance to disable telemetry features within the preferences dialogs. See [2], [7], [8] and [9].

As these privacy impacting features are enabled by default, before first launch of Firefox on Linux, you should disable these third party and telemetry features and also lock down other security and privacy settings. See [10] and [11] for the method of doing so, and an example user.js that contains decent documentation on well over a 100+ recommended configuration changes to make Firefox more respectful of privacy and security. If you don't reconfigure a user.js before first launch, at least the "New Profile" event will be notified to Mozilla with the unique client ID after a delay of only 30 minutes from creation of the first Firefox profile[9] (first launch).

[1] https://glandium.org/blog/?p=3923

[2] https://github.com/mozilla/gecko-dev/blob/HEAD/build/moz.con...

[3] resource://gre/modules/URLFormatter.jsm (use within Firefox URI bar)

[4] resource://gre/modules/AppConstants.jsm (use within Firefox URI bar)

[5] https://gitweb.gentoo.org/repo/gentoo.git/tree/www-client/fi...

[6] https://github.com/archlinux/svntogit-packages/blob/packages...

[7] resource://gre/modules/ClientID.jsm (use within Firefox URI bar)

[8] resource:///modules/BrowserUsageTelemetry.jsm (use within Firefox URI bar)

[9] https://github.com/mozilla/gecko-dev/blob/c3ec016fafa4cea6a0...

[10] https://kb.mozillazine.org/User.js_file

[11] https://github.com/arkenfox/user.js/