This seems to be a recent behavior.
I use Google to log in to SO. In my normal browsing browser, I don't typically remain logged in to Google. So, if I need to (rarely) log in to SO, I will click the Google link, connect in to SO, and, then, fire up a new window, bounce over to Gmail, and log out of Google.
Before, I would retain my SO login, but be logged out of Google.
Is there a new setting that I need to check to disable this? I've seen other posts where folks want to log out of SO and have that log out of Google as well, so I can see there needing to be flexibility on this. But I would mostly prefer to not have a persistent Google log in if I can possibly avoid it.