Per coveryourtracks.eff.org, just my HTTP headers leak 18.46 bits of information, which seems to be the most the tool can report? Presumably most of that entropy comes from my language settings (en-AU,en;q=0.9,de-CH;q=0.8,de;q=0.7), so the only way to be not fingerprintable is to give up on smart localisation.

If people have a problem with fingerprinting, they need to focus on making it illegal to trade data tied to fingerprints, not trying to make users all look the same (we aren't!).