I wouldn't think that your computer, or Firefox, or this site would know whether you were in a strange state or not, so that's probably out

I almost always use Firefox to come here and I've never had that happen, so it may not be Firefox either.

Something that used to happen to me at another site was that links, as well as my bookmarks, would work either with or without the "www". However, everyone's login cookie would either have the www or not, depending on whether they'd gotten to the site with or without it. The catch was that if I posted a link with the www in it and someone else who'd logged in without the www clicked on my link, they'd get logged out. The same would happen if my link didn't have a www but their login cookie did.

I'm pretty sure we get (and stay) logged in through cookies here, so when you investigate you might want to see if there's any way that what you're clicking on could conflict with your login cookie. It may not be the "www", though; I've never seen the www on any of the URLs here and when I tried inserting it in one I got a "404 page not found".