The mustache thing is a myth. If it was ever a rule (and that's open to debate), it was enforced selectively. Just like the rest of the rules.

I think that Italian men in general (and by extension, some Italian American men) just shy away from facial hair. If anything it was probably a cultural thing that wasn't mutually exclusive to wiseguys being clean shaven. But like I said, there have been plenty of guys with facial hair over the years. This topic comes up all the time. If you put mustache or beard in the search you'll get a bunch of hits.

And welcome to the board.