Replace the bracketed [...] placeholders with your own information.
http://video.foxnews.com/v/1241186546001/?#sp=watch-live
Recently (first noticed 9/28) Foxnews.com live player is not loading. Fox recently updated their video player to show a live preview (~10 minutes) before you sign in so it could have something to do with that.
Gist of the logger: https://gist.github.com/AlexMcArdle/29fb524e51d66597596de617457ed2e0
Provided gist above. Not working in Firefox either.
add
||cdn.krxd.net^$script,redirect=noopjs,domain=video.foxnews.com
@@||global.fncstatic.com/$script,domain=video.foxnews.com
https://insider.foxnews.com/2019/01/15/judge-andrew-napolitano-bob-mueller-sole-issue-william-barr-confirmation
Video won't play

EasyList is the issue. Haven't been able to narrow it down to what filter exactly yet.
does this work for you ?
@@||video.insider.foxnews.com/$script,1p
No.
@@/ima3.js fixes it. (log shows: https://imasdk.googleapis.com/js/sdkloader/ima3.js)
No ima3.js request for me using european ip.
Only using us ip I get the issue.
https://www.foxnews.com/opinion/judge-andrew-napolitano-can-congress-amend-the-constitution
or
https://video.foxnews.com/v/6013531300001/#sp=show-clips
Video won't load.
@@||foxnewsplayer-a.akamaihd.net/player/*$script,domain=static.foxnews.com
Problematic rule is /prebid/* in EasyList.
The whole directory doesn't need to be whitelisted.
How about @@||akamaihd.net/*/akamai/amp/prebid/*$domain=foxnews.com and @@||akamaihd.net/*/akamai/amp/react/*$domain=foxnews.com because those are the only two directories the player needs to work.
@@||akamaihd.net/*/akamai/amp/prebid/*$domain=foxnews.com
That works too.
@@||akamaihd.net/*/akamai/amp/react/*$domain=foxnews.com
That doesn't.
I can't reproduce, the video works fine on my end at both example links.
There is no /prebid/ request on my end.
Here's a screenshot of the rule blocking the URL that is needed:

What I meant in https://github.com/uBlockOrigin/uAssets/issues/729#issuecomment-531070326 is that you could add ||akamaihd.net/*/akamai/amp/*$domain=foxnews.com and the only directories needed for the player to work (in my testing) are prebid and react.
Well, we get served different documents, so I can't reproduce the issue in the first place.
Let's call this fixed for now.
https://video.foxnews.com/v/6083433910001#sp=show-clips
Video doesn't load.
@@||static.foxnews.com/static/isa/app/lib/VisitorAPI.js$script,domain=static.foxnews.com