Catholics in Italy don’t drink from the same chalice in any part of the religious ceremony, for hygienic reasons, since the 12th century. It is sometimes done during specific rites (on Easter Vigil, I think?) but it is not widely used at all. It might be something that is done outside of Italy, but I’ve never seen it done here. That said, attending Mass can surely spread the virus — but just because many people gather together in a confined space. That’s why churches in Italy have been closed (or partially closed) for weeks.

Edit: since the 15th century