Firefox 42+ has a Tracking Protection feature that is enabled by default in Private Browsing mode. When you are in private browsing mode then Firefox can show a shield icon at the left end of the location/address bar that some content is affected.

You can disable this feature in "Options/Preferences > Privacy" or via the about:privatebrowsing page that get when you open a New Private Window.

• Options/Preferences > Privacy: "Use Tracking Protection in Private Windows"

• https://support.mozilla.org/kb/tracking-protection-firefox
• https://support.mozilla.org/kb/control-center-site-privacy-and-security-firefox

If you use extensions (3-bar button/Tools > Add-ons > Extensions) that can interfere with loading content (e.g. Adblock Plus, NoScript, Flash Block, Ghostery) then make sure that such extensions do not block content. There is security software that can interfere with loading content, so check that as well.

• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

The websites are viewed with Private Browsing Mode switched off, so that can't be the reason.

The pages load perfectly in Microsoft Edge, and in Firefox I turned off the security apps to make sure, to no effect, so I suspect this is a browser issue.

Did you try Safe Mode?

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

• Switch to the DEFAULT theme: 3-bar button/Tools > Add-ons > Appearance
• Do NOT click the "Refresh Firefox" button on the Safe Mode start window

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Hardware Acceleration isn't switched on.

As for Safe Mode they run in that, but unfortunately that's the only way the sites want to work properly; running Firefox normally with all add-ons deactivated still won't let certain media load correctly.