Website says enable cookies even though they are enabled, on Catalina
If there's any hint of "best viewed in these browsers" on the site, it's good to use them. 

You can "empty cache" using alt+command+E or by using Develop Menu in Safari.

Also, try turning off "Prevent cross-site tracking" to see any effect. You can turn it back on later, if you want.


  Some websites use third-party content providers. A third-party content provider can track you across websites to advertise products and services.
  
  With this option turned on, tracking data is periodically deleted unless you visit the third-party content provider.


https://support.apple.com/en-in/guide/safari/sfri35610/12.0/mac/10.14.5

Also disable all extensions and third party safety applications you might have.