After avast update I started experiencing problems connecting to certain websites namely google.com and apple.com, app store, and some others, others were ok, disabled browser protection and site have no problem.
I would guess your network has broken IPv6, which causes the problems (it’s not a big
issue without Avast - except performance - because the browser normaly does a reconnect
to the servers IPv4 address which is not possible with Avast webshield enabled) If you disable
IPv6 support in the Avast webshield preferences, things will most probably get fixed.
If not, some more info is required, at least the relevant parts of the system log file.