The major cultural differences are between Northern and Southern Italy. The North was part of the HRE for a thousand years, while the South was part of Byzantium for almost as long. There's a lot more Greek and Arab influence in the South, German in the North. A lot of Northerner's don't consider Southerners true Italians. The reason the Nothern Alliance wants to split away, however, is economic, not really cultural, though as in so many cases, economic causes are overlaid with cultural overtones. Bascially, the inudstrialized North is tired of subsidizing the agrarian South.
During the period of EU2, Adriatic Italians on the East side of the Adriatic didn't seem to see a split between Venetian and Italian. When Venetian holdings fell, Italians were more than willing to go to the Kingdom of Naples rather than Venice.
As well, the Italian city-states and the Pope seemed to treat Venice as just another Italian city-state, albeit one which was not part of Imperial Italy. The question for seperating Italian and Venetian culture should rest on a couple questions.
Would Italians have had difficulty in ruling Venice and it's possessions?
Would Venice have had difficulty in ruling Italy?
Is the difference between Venice and Italy greater than between Northern and Southern Italy?
I would argue the answer to all three questions is no, and thus a seperate culture is not justified.
In addition, what does the splitting of culture serve? It's exceedingly unlikely that any ai Italian state is going to take Venice. Venice, with all it's islands, is a bear to take down. Since Venice would also have Italian state culture, it wouldn't stop the reverse, Venice ruling large swaths of Italy (not that lack of Slavonic stops them from ruling large swaths of the Balkans). The only non-Italian states to have Italian state culture: Athens and the Knights, aren't likely to take out Venice.