- Zap that element (uBo element zapper or custom CSS style rule via Stylus).
- Globally deny ALL cookies for that site, via uMatrix.
Note that uMatrix (and AFAIU Fireox) already block all third party cookies. This just makes that prejudice global to the site itself.
The number of sites for which I require some level of state preservation is parlous few. Hacker News itself is most of them, my Fediverse home the other.
(I largely don't use the Internet for commerce. That's always struck me as a bad idea, getting worse. If I cared ... another very small number of exceptions would deal with that.)
Sometimes it breaks youtube/twitter embeds.
I've rejected all optional cookies/tracking for many years and I've never noticed any missing functionality.