I'm sure that was Amnesty's mistake with the cookie prompt, but basically if you hit the option to customize what cookies are set, it won't let you read the page, it just won't work.
Honestly, a prompt on every site is probably not a good way of conveying consent.
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I don't understand why sites don't just use the DNT header (which has been around for ages) or something to say "okay, this user doesn't want these extra cookies".
For something like analytics, maybe there could be a DNTA header which clients / browsers could use.