I am observing same behavior in Safari. I checked my wife's installation and the option is not a default option as it seems. The certificates are not installed at all.
How do I check my system key chain and whether avast has installed those certs?
How do you know, that the certificate is not installed, if you do not know where to search for it?!
The list of installed certificates can be inspected using the "Keychain Access" utility. A certificate
named "avast trusted CA" should be in the "System Roots" keychain. Moreover, it must be the
same certificate as in the file
/Library/Application Support/avast/config/certs/cacert.pem.
The tech info does not explain why I am getting those pop ups about unknown avast CA.
Well, the technical info is definitely not aimed on ordinary Mac users. It shall explain the network
shield principles to advanced users and system administrators and help them to solve such
issues. There is definitely something wrong with your avast! installation, but unless you are an
"expert" (who can diagnose the problem with some hints like the techinfo), the best way for You
to get avast! working properly is to uninstall it and install it again.