Does this mean you cannot install Firefox anonymously?
Not a good look lol, firefox has been speedrunning getting rid of all it's users the last few years. For now at least, the versions shipped with linux distros will all have the same identifier and generally tend to have some other tracking options disabled by default.
Maybe that is the real reason Google pays them to be the default search provider, to wreck the project.
Mozilla basically exists at Google's whim so they can point to it and say they don't have a browser monopoly
If it bothers you enough, you can download FFox from here without a unique id in the setup.exe thing. https://ftp.mozilla.org/pub/firefox/releases/
or get it from your distro's repository, which of course doesn't use the installer
