Super strange. I apologize if you tried these already but I have some quick ideas to run by you.

• Did you try changing your internet setting inside Firefox to "No Proxy"?

Firefox menu button > Settings > General > scroll all the way to bottom of page > Network Settings > click "Settings" button > choose "No proxy" > click OK button to save setting

• Do you have a VPN installed? Try disabling it then checking the affected sites.
• Do you have a AV running inside Firefox? Check the Addons section to see if there is a antivirus addon. If there is, disable it or uninstall it if you don't need it. See here: Disable or remove Add-ons
• Delete all cookies. The cookies.sqlite file may have become corrupted and when you visit these sites they see a corrupt cookie then either go blank or throw a error message. Maybe this file has to be found and deleted itself. Or you can make a copy of it to back it up then delete the cookies.sqlite to see if that helps. This must be done while Firefox is closed though.
• Disable all addons and revisit the sites. Maybe a addon is doing something weird that is causing the sites not to display.

Is this happening to all websites you visit? And when they don't load, the page just stays white and blank?

I'll keep thinking up more ideas but it seems like something (antivirus, malware protection, firewall, etc) is intercepting the internet connections. NordVPN's Threat Protection/Web Protection, Malwarebytes BrowserGuard, AVG/Avast, etc. all have something that hooks into the browser and tries to block websites it doesn't like. Sometimes they receive bad updates that say good websites are bad and block them from loading.

Sorry for the late reply.

I have swapped over to "No Proxy" with no effect. I don't have a VPN, Not yet, anyhow. I've removed all my add-ons, so an antivirus or regular addon isn't the issue. I've just deleted one Cookies.sqlite, but the errors persist, should I delete the other cookie.sqlite files too?

And most websites, (With the exception of Mozilla websites) seem to be completely blocked off, Not a white screen loading, but it seems like the Firefox browser just isn't connecting to them at all.

Appreciate the help!