Even when entering a shop, bar, restaurant or post office or bank, it is mandatory. Just as it is necessary to wear gloves in the supermarket and in food stores. Or if you go shopping for clothes.
Furthermore, several regions have imposed more restrictive measures. Until now, masks are mandatory even outdoors in Sicily, unless motor activity is performed. Ditto in Sardinia, “where it is not possible to maintain the spacing of at least one meter”. Even in Lombardy until 14 June it is mandatory outdoors as well as indoors. The ban expires on 1st June in Veneto and 3rd in Piedmont. In short, before moving from one Region to another it is better to inquire.