This is a good time to remind people that these prompts not only concern cookies (or even all cookies), but any form of non-essential visitor tracking.
Some tracking methods will more effectively be able to track you across the boundaries of your "incognito" sessions.
For example, the modern browser has a huge API surface that makes accurate finger printing using tuples of individually only moderately narrowing information possible for as long as you allow it to execute JavaScript.
I use separate and fresh isolated firefox (running within podman container) to make fingerprinting a bit more difficult, it's still fingerprintable and probably this new fingerprint can be easily associated with the other but I like to imagine I make it more difficult to track me. Every little helps :)
I do wonder how accurate that is these days... Like it says that my user agent is significantly more unique than my monitor resolution, but Safari froze the user agent years ago.
Which means that they calculate there are 21x more people that have a $5k XDR display than use macOS Safari. Which seems... unlikely.
(anyway, tracking via IP address is a pretty accurate way to track across browsers and cookie resets, until you're behind a large NAT / proxy.)
Yep, with this much of information it probably won't be a problem to match two browsers running on same machine. Interestingly my ff session which runs in podman does not reveal most of the best sources of fingerprinting which I can see when running the same test on chromium.
I wonder if the answer to the problem could be to let those companies to track whatever they want if only all they get is exactly the same fingerprint from every user.
They could still fingerprint your browser. Agreeing to the prompt doesn’t just mean consenting to the placement of cookies but potentially the combination, re-identification and sale of such data.
After I'm done reading I just close the website again.