Yeah, that pic is the one I was referring to, it's hard to tell if it's a mustache or just one beginning to come in. I know Cali' was always a clean shaven guy.
There's always exceptions, even in Italy, but in the end it still comes down to just being a cultural thing over there. Nobody tells them they can or can't have facial hair, but many do see it as sloppy, even today.
Off the top of my head, I know Antonino Lo Nigro had a mustache, both Lo Piccolo's father and son, Gianni Nichi had a goatee thing going on for a while. There's been a few.