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If I can't opt out in two clicks, I leave the website and click the next search result.

Yeah, but that's kind of a pity if this one was the official documentation...

Or I just right click open it in private mode

No guarantee that they won’t track you through other fingerprinting methods.

When do you ever have that guarantee anyway, though?

I'm not a statistician, but I'd think the less they can fingerprint you, the more you go in the "noise" bucket.