Adguard is currently incompatible with Apple's Private Relay. You'll need to go to System Preferences and click on Apple ID. Then uncheck Private Relay. Adguard will work after that.
Adguard -- Application version 2.5.1.906 nightly (CL-1.7.131)
Big Sur beta 10
Yay, oh yay! Seems to fix all my problems with Twitter in Safari. You made my afternoon!
Also, YouTube is finally working again.
EDIT:
Sigh, hours later, the Twitter problems are back. They usually clear by quitting...
Bit Sur developer beta 9 -- Adguard worked with Safari (with some glitches on twitter).
Big Sur developer beta 10 -- Adguard utter failure to connect to ANY website with Safari. Uninstalled and re-installed Adguard but, no joy. Disabled Adguard extension for Safari but, no joy. Firefox works...