I am not sure if the site owners can fix it or if it's an issue with BBC Code itself, but basically below is the code that the site spits out when you use the youtube bbc code :
The code needs to spit out
https: instead of
http in the highlighted section above. Possibly the site admin might be able to tinker with the Content Security Policy and get it to work -- not sure.
Basically, from what I understand, as new versions of browsers have been introduced, security has been tightened and some web technologies, such as BBC Code, have not caught up yet...
NOTE: This is also why if you try to post an image and your image link starts with http instead of https, your image will not show. This is one of the reasons I like
https://postimages.org/ for image hosting. --
they give you a https image link. . You just drag on drop your photo(s) onto the upload page and you get a link (or links).