Considering the amount of variables that contribute to the browser fingerprint, you would be forced to conclude that the only way to prevent being so unique is to run a browser in a vanilla VM (although the OS is already a variable in itself).

I think this is a topic that gets discussed by (for example) the Firefox developers, but I get the feeling that this is one of the hardest problems to fix.

I would like to see a browser mode akin to the privacy mode most browsers feature that reduces the number of identifying variables (at the cost of features). So instead of telling the world that my time zone is CET and I prefer English (GB) as language, it would select a random time zone and locale (although this does inconveniently mean that sites might suddenly serve me content in Portuguese).

Come to think of it, TOR Browser probably does a couple of these things. Disabling Javascript is surely the biggest factor, although that does make the modern web pretty much unusable.