I have several different gmail accounts which all work perfectly with Firefox Quantum as webmail (although I generally use Thunderbird with IMAP for them). I just tried a couple of them and they are fine, but I have the passwords saved and I use a Master password. I wonder if the popup blocker might be causing a problem? I do have an exception set for it as www.google.co.uk (see snapshot and Options -> Privacy & Security -> Permissions and Exceptions button alongside "Block Pop-up windows". You could just try going to your local google main search page, logging into Google there then clicking the Gmail link at the top right of the page. If you can log in there, your gmail should connect fine.