Earlier quoted context omitted.
If I understand it correctly, the way this fingerprinting works is just by using questions you need to show the website properly. 'What is your screen resolution? What HTML5 features do you support? Do you have this font/plugin?' Bar giving up all those facilities, the best you can do is ask and hope they comply....
There's browser extensions that will fake all of those to a standard value. The tricky part is that with fingerprinting, depending on your chosen faked value you could end up being more identifiable, if not enough people use it. For instance, you can change your user agent and headers to some generic Windows Chrome one but a savvy tracker will fingerprint your TCP connection and realise you are actually on a Mac, and…
It would be interesting to see some reports on that question. Of course, the Law would never abide such accountability, but one can dream...