I am not "signed in" to Microsoft.
I always go in to my desktop as a Guest, never as an administrator. - Thanks to advice from Mixture.
So I don't sign in to MS, don't sign in to Firefox, and do not currently have any issues with gmail.
I have set Firefox to delete everything when I sign out. Even pprune i.d. and flyertalk i.d. - which means if I want to comment, I have to sign in again, but only to specific websites.