I realise that being in the UK this may be of little interest but must someone in UK running Catalina with BT internet.
I think the problem revolves around Flash (which BT insist on using) and the 'use flash on this site' seems to have gone. Also the security instructions on the B~~T site are out of date (referencing Mojave).
My Dad has upgraded to Catalina and is a frequent user of BT Sport on his 2014 MBP. He has had no problems as far as I can tell. And it would be me that he would get onto if he had... Sorry can't help further.
As someone said it’s around the use of flash, if you go into safari settings and add the BT site to authorised use of flash it should work, I’ll take some screen shots later when the house is awake If that’s helpful?