I strip the referrer generally via https://wiki.mozilla.org/Security/Referrer, unfortunately it breaks a small number of sites very badly, such as web.archive.org and a few others. some of them claiming it was done to combat scraping.
Breaking is only part of the problem. The pages that rely on the referer header take it for granted and do not implement any meaningful error handling. They just die a horrible death, instead of responding with an error message stating that they need a referer.
One bad example is relying on the referer only for log-out, everything else works. That site also runs massive js on log-out, as if it really needs to rely on explicit log-out, and not just the user disappearing.
I have never considered faking or suppressing my referer header. I don't know why I would care. I suspect I'm in the company of well over 99% of all internet users.