I tried librewolf to see if it reads /etc/machine-id. It does not. At least not to my trials so far. I used the strace cmd to watch it. I tried when starting librewofl. And again when loading various sites.

LW does read MANY font related files from /etc. That could be a fingerprint ofc. Esp if a site reads back the canvas! Fonts are a majority of what LW reads from /etc. LW also reads /etc/os-release. IDK what it does with that. That file does not have a unique machine id, but it ids your OS and version. There are a few others too. Like /etc/localtime.

IDK about Firefox. I didn't try it. Maybe it would be much worse. Someone can try and report here about it?

My guess is, every normal browser can be accurately fingerprinted. Even with fingerprint resistance like FF forks. Esp if JS is enabled!! There are just toooo many ways. ID resolution services are used by most big sites now. They employ very smart and clever data scientists. I doubt we can block every method they have, in a good enough way.

Tor Browser tries! But that is blocked by sites that use identity resolution. Also, TBH I don't even believe Tor can block enough fingerprinting. Some like TLS fingerprints are not even blockable by a browser.