Would it be possible to build a Firefox plugin that creates and isolates the requisite cookies to allow reputation to be built, but at least partially maintains privacy?
I was thinking maybe something that has 10 difference Google sessions, and shards them depending on the website, deciding which to send to the Captcha. You'd build reputation at 1/10th the speed, but you'd still potentially build it. Or, one that allows you to create a random Gmail account and then use that as your identity across the different sites. Perfect privacy would be hard, but improved privacy should be doable.
Alternatively, getting something like blinded identity tokens widely used would be good.
I doubt it's easy, so I prepared such a setup myself, i.e. I keep a separate browser with a Google account and use it only when I really need to. Helps in cases like this one, but of course you give up some privacy - hopefully just the minimal bit.
I'm fairly sure (but admittedly not certain) that captcha uses non-cookie and non-account based methods for identifying users, so I don't those methods would work.
I was thinking maybe something that has 10 difference Google sessions, and shards them depending on the website, deciding which to send to the Captcha. You'd build reputation at 1/10th the speed, but you'd still potentially build it. Or, one that allows you to create a random Gmail account and then use that as your identity across the different sites. Perfect privacy would be hard, but improved privacy should be doable.
Alternatively, getting something like blinded identity tokens widely used would be good.