I never installed the SafeZone browser as I was using the (free) avast business cloud version.
There are multiple posts/threads on this webboard about it.
Most are from right after avast rolled out the SafeZone Browser to the users of avast free (without any notification).
As for the (really old now) SafeZone, I saw it with every new version released after it was removed.
I can't test things now as I have removed everything from avast from my systems.
I don't know if it is still the case, but I remember the browser plug-ins where also still in their folder after de-selecting them through the control panel > programs > avast > change
They don't do any harm, but people don't like to see that if they have chosen not to install/removed the option.
People say "I removed them, so the files/registry entries for them should be gone".