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Their website (https://coveryourtracks.eff.org/learn) do mention the concern you have; Blocking trackers means you are a user with a very specific privacy settings. I suppose it would be like going around with a full face mask; You are technically private, but you are uniquely identifiable unless someone else does that. I also get “Uniquely Identifiable” on my personalised browser, but nothing like it when I try it out on newly installed Mullvad browser with no changes.

Not that I know much about how Tor traffic is identified, but Tor bridges seems like a potential solution? I would dig into that a bit more.

Not money, but fucking vouchers.