When Avast’s Web Shield is activated, eventually I get logged out of my iCloud somewhere (usually on iTunes, Mac App Store, or System Preferences), and when I try to log back in, I get the message, “There was an error connecting to the Apple ID server.”
As soon as I disable the Web Shield, I can log in. Reactivating the Web Shield doesn’t cause problems at first, but eventually I’ll get booted out again. It’s really frustrating.