The scene of two furry creatures performing an operatic song in gibberish was unusual for the Muppets as the "puppets" used were actually two of the performers' chins; Jerry Nelson and Jim Henson to be specific. Eyes and noses were attached beneath their mouths and the bodies were attached, upside down, to their faces and the whole sequence was shot upside down and then matted onto the background by way of an early form of "green screen" technology. The performers' natural beards served as the characters' fur.
'Pigoletto' is, of course, a play on the well-known opera, 'Rigoletto,' by Verdi. Verdi also wrote 'La Traviata,' which is where the music for 'Pigoletto' comes from.
The closing number, 'Pigoletto' is a mishmash of several operatic tropes and references including Piggy as Cleopatra from Anthony Barber's 'Anthony and Cleopatra' and pigs in Wagnerian costume singing Italian opera.
In late February, 2021, this became one of 18 Muppet Shows to get a content warning on Disney+, for "negative depictions and/or mistreatment of people or cultures".