Earlier quoted context omitted.
https://panopticlick.eff.org/ You'd be surprised.
Not really. Currently, we estimate that your browser has a fingerprint that conveys 11.9 bits of identifying information.
The amount of information conveyed by the HTTP_ACCEPT headers is especially preoccupying. There is nothing in there, apart from maybe the language, that should leak any info, on a modern browser. And certainly not 10 or 16 bits of info.