Every site shown in google search shows the Avast safe icon, though both McAfee and Webroot have shown these sites to be unsafe. This makes me think this Avast service is not working, or at least not working properly. Somewhat unsettling.
Are you speaking about the Avast Online Security plug-in?
If you are you can safely remove the "browser protection…
Control Panel>Uninstall a Program>double click “avast”>click “change”>untick “browser protection”>reboot.
FYI, I don’t have it installed. I rely on the three resident shields for my protection.