In had the same issue with Firefox, while other browsers worked with the CallProtect facility. All other functions on BT's MyAccount worked with Firefox. It seems that the ad-blocker Ublock that I am using with Firefox was causing the problem. The solution was to add BT's site to the whitelist on Ublock. Strangely, Firefox did work with CallProtect for the first few weeks.
As JB2016 has pointed out, any number of browser extensions are likely to be getting in the way of accessing these services so do check what you are running.
I had the same issue a couple years back on BT.com as well as a banking site and it was driving me nuts until I finally figured it out.
I have also found a problem with BT Call Protect online support. I use firefox which is an industry standard but have also tried Microsoft Edge and again just get the three bouncing balls. This is clearly a fault which must be sorted. I can't understand why BT are taking so long as this has been down for weeks. When I log in everything else works so it is not a browser issue and the people at 0800800150 agree it is a fault. Please get it sorted - at the moment BT Call Protect cannot be used properly.