Who is allowed to enter a street sign-posted like this?

Your answer is correct. This traffic sign indicates a general entry prohibition for vehicles, but the additional plate "Anlieger frei" means that access is allowed for residents (Anlieger) and people visiting them or those who have legitimate business there. Through-traffic, or vehicles that just want to pass through without any connection to the area, are not allowed. This rule helps limit traffic in residential or sensitive areas to only those who need to be there.