A few guys (Jimmy Marcello and Tommy DelGiorno) managed to "pull the wool", so to speak, in that they were only half Italian. And Stanfa (for whatever reason) decided he'd "make" Veasey, who was Italian on his mothers side. I think Chucky Porter was another one. John Gotti famously broke the rule to induct his son.

But as Ivy's says, it seems that nobody who wasn't at least part Italian ever got made.