I know that putting 16th-century characters into our contemporary understanding of politics is way beyond absurd, but I want to do The Taming of the Shrew just because I can.
I'll try to approximate characters to the 21st century. I'll also be very wrong.
I want to bring this back but using the 2022 Italian election because after all the play is set in Padua. I guess this version will use slightly different vibes.
Baptista is a wealthy and very conservative professional so he seems like an obvious FdI voter.
Bianca definitely voted Azione/Italia Viva because her personality suggests shallow, performative liberalism, while
Katherina as a rebel from this sort of family starts as a Green-Left voter but after her taming she presumably adopts Petruchio's politics... and
Petruchio is the male chauvinist we all know but also a fairly well-off (and presumably educated) young man so I get the feeling he might vote Azione.
Lucentio is a vain liberal arts student so he goes for AVS, or in any case definitely the centre-left coalition.
Grumio and
Tranio as I mentioned in my original post are hard to fit in the contemporary world but the characterization I used means they'd likely go for the M5S.
Gremio is an unpleasant old man lusting after women less than half his age, which makes him almost too obvious a fan of Berlusconi, although I can see him even better choosing Lega in particular.
Hortensio is a complete loser so of course he votes PD.