As a user I don't want you to know that information. I wish there was a way to click on links with the referer field removed entirely from the request(maybe via context menu)
Yes, it strips off for any URL.
For only third parties, I believe 'network.http.referer.XOriginPolicy' is the relevant flag (haven't tried it out myself).
I use RefControl in Firefox. I've set the default to be the root of the destination site. That is, for example, clicking a link to https://foo.com sends https://foo.com as the referrer.