There is security software like Avast, Kaspersky, BitDefender and ESET that intercept secure connection certificates and send their own.

https://support.mozilla.org/en-US/kb/firefox-cant-load-websites-other-browsers-can

https://support.mozilla.org/en-US/kb/firefox-and-other-browsers-cant-load-websites

https://support.mozilla.org/en-US/kb/secure-connection-failed-error-message

https://support.mozilla.org/en-US/kb/connection-untrusted-error-message

Websites don't load - troubleshoot and fix error messages

http://kb.mozillazine.org/Error_loading_websites

What do the security warning codes mean

This didn't really solve the problem as the site is loading fine - it's just the login feature that wasn't working. That said, the login feature is working today in both Firefox and Chrome. So, I'm not really sure what the issue was but it's no longer there.

This issue can be caused by corrupted cookies or blocked cookies.

• check the permissions for the domain in the currently selected tab in "Tools -> Page Info -> Permissions"

Clear the Cache and remove the Cookies for websites that cause problems via the "3-bar" Firefox menu button (Options/Preferences).

"Remove the Cookies" for websites that cause problems:

• Options/Preferences -> Privacy & Security
  Cookies and Site Data: "Manage Data"

"Clear the Cache":

• Options/Preferences -> Privacy & Security
  Cookies and Site Data -> Clear Data -> Cached Web Content: Clear

Start Firefox in Safe Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration or userChrome.css is causing the problem.

• switch to the DEFAULT theme: "3-bar" menu button or Tools -> Add-ons -> Themes
• do NOT click the "Refresh Firefox" button on the Safe Mode start window

• https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-using-safe-mode
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems

You can remove all data stored in Firefox for a specific domain via "Forget About This Site" in the right-click context menu of an history entry ("History -> Show All History" or "View -> Sidebar -> History").

Using "Forget About This Site" will remove all data stored in Firefox for this domain like history and cookies and passwords and exceptions and cache, so be cautious. If you have a password or other data for that domain that you do not want to lose then make sure to backup this data or make a note.

You can't recover from this 'forget' unless you have a backup of involved files.

If you revisit a 'forgotten' website then data for that website will be saved once again.

• https://support.mozilla.org/en-US/kb/delete-browsing-search-download-history-firefox