How can I hide my logged in sessions from other websites?

Most people go on browsing the web while connected to their facebook/gmail/etc. accounts. These websites somehow know what accounts you're logged in.

For example, if you got to hide.me's torrent page, it will tell you what logins of your were detected, even though you never (explicitly) approved this website to access your account.

I know that switching private browsing and/or using extensions such as Ghostery help in some ways, but is there a more straighforward way to block this?