I never could get betfred.com to show up at the home page, despite temporarily allowing *everything*. There's a good chance that that is because the site blocks certain things to US IP addresses, since our lawmakers, in Their Infinite Wisdom, have decided that we are not capable of making our own decisions regarding gaming.
However, it does appear that betfred is indeed run by connextra, and so you will need to allow the latter.
I went directly to betfred using your link.
How do I find out which 3rd party scripts are needed (if any)?
This is often a matter of trial and error, since some sites are coded in a very complicated matter. This is one of them. You start with the minimum possible allowance (none), then the site that you are on. Then, if things still don't work, you allow one by one until they do, starting with the most likely candidates.
Since betfred seems to be run by connextra, that is a logical first choice. Please keep in mind that I'm not aware of what the site is *supposed* to look like. Normally, I would set up an account for test purposes, but I didn't think they'd let me register from a US IP. This was confirmed when the registration form "Country" did *not* list the United States.
I still think I can help you -- sort of. Betfred is another in a trend that is a pet peeve of yours truly. When you allow one script or object, or even if you allow them *all*, after the page reloads, new scripts and/or objects try to run. This can go on for several generations of page reloads, and I find it very annoying.
After allowing multiple generations in this fashion, the only one left was google-analytics.com, a tracking service. Any site wants to be paid by its advertisers for page views, of course, so some will refuse to function unless you allow the GA script. However, there is some privacy leak there. For this purpose, NoScript developer Giorgio Maone created a
surrogate script that will satisfy the site without sending any of your personal data to Google.
So you will want to do some experimenting to see what is the minimum permission needed for the function you want to work.
Please bear in mind that we have no way of knowing whether the scripts or domains in question are safe. You would have to do your own investigation into the reputation of each site whose scripting you allow.
WOT is one possible place for assistance.
I hope this helps. Cheers!