No credit card. You have to send a $1 bill by snail mail, which is proof of "work" (mailing the bill) as well as $$. You enter the bill's serial number when you enroll the account, and the account activates when the bill arrives. You can be pretty anonymous this way.
I once proposed a scheme like this where you would donate to charities who would post lists of serial numbers they had received, for this purpose, but it never got anywhere. Maybe we need it more now than we did then.
I guess instead of mailing a $1 bill, if necessary it could be a hand drawn picture of a kitten (artistry not required). Authentication would involve checking the paper for pressure marks made by the pen. I wonder how many would take the trouble to fake that.