In the end I made it work, but I am still not sure what was the problem. I rememeber I had to clear the cookies in Firefox. Then after deactivating and reinstalling this plugin it was all fine.
Also, when activated only for specific sites separatedly, it happened to me, that for no apparent reason I got 404 redirect when I entered the right credentials and clicked ‘Login’ while I was on the right url …/dwd54d55d4a5xx/
