Eating and walking. A no-no in Italy but not in Sicily???

Eating and walking is absolutely normal in Italy, do you think that pizza, focaccia, porchetta sandwiches and lampredotto were created to be eaten sitting in restaurants? Camping out of parks (i.e. on monuments and in squares) is frowned upon and often forbidden. Again: camping, not eating.

Even if, nobody cares what tourists do. You are not "real persons" that can Actually violate social customs.

I think the issue in Italy is more about blocking a thoroughfare or viewpoint in order to make a little picnic - this is what's frowned upon.

different rules in Venice though, eh?

Arancini, delicious cheesy rice balls, are definitely Sicilian walking food. You’ll be allowed to sit at a table or counter from the place you got yours, if it has one, and if you were so inclined.

Yes, where there is street food there is eating and walking. However, oftentimes people get their street food and then stand/sit nearby to eat it. The markets are full of stalls with a small counter or picnic table in front, and also full of clumps of people standing around chatting and eating food they picked up at the stands. So they are eating street food outside, but not walking. I’d say even in Sicily eating and walking is less common outside of the market area. If there’s a food cart, people will more often take that food and hang out somewhere to eat it instead of walking all over with it. Not that it’s never done, of course. Just not super common.

Who cares what the rules are. You're not from there. You're on vacation

Well, that is the type of attitude that can get you in trouble for one, sometimes people do care.

Venice, Florence, and Rome (off the top of my head) all have at least some prohibition on food and drink in public to a degree, so worth asking about.

I don't recall anything official, but as long as you do not block the flow of movement, make a mess, or imply disrespect (sitting on Church steps, fountains, monuments, etc.) and take your cues from those around you, you should be fine. It would be more common near the vendor, or in the market, less common wandering the streets, and not advised on Public Transport.

remember to use the paper provided. You will be marked out if you don't and use your fingers to touch the food.

Nigel, don't be MontyPythonesque! They could believe you are serious.

It's not just in Venice, Florence and the cities oh the tourists' path: nobody gives what you can imagine if you eat while walking, running or doing cartwheels. On the other hand camping on stairs, fountains and monuments is not just a matter of respect: IT IS FORBIDDEN and you may be fined by local police. If one was allowed to pic-nic on a 300 years old fountain, everybody would expect to enjoy the same right and the fountain would be constantly under restoration. Really, it's not that difficult.

I understand sitting and eating, or standing and eating. I don't think I've ever seen anyone walking and eating TBH. I'm not sure I could do it. Am I misunderstanding what you mean?

People seldom walk-and-eat because is a little difficult to cope with it. :-D Can be done with something small, but if you have a medium size sandwich and a bottle of water is just a little tricky.
I believe you can see much more tourists eating walking because locals know much better where to go to sit. For example in the covered market in Modena (Mercato Albinelli) there are a lot of choices for street food and tables around: some tables are reserved to some sellers, other are free. A tourist maybe is puzzled and not sure, so don't sit down to avoid misunderstanding.

Who cares what the rules are. You're not from there. You're on vacation
"Well, that is the type of attitude that can get you in trouble for one, sometimes people do care."
Rules are important everywhere, even because often are related to local laws. In USA for example I suppose is illegal walking free and drinking a bottle of beer or wine on the street.

When in doubt, start with a gelato! Strolling with a gelato is acceptable.

simply a supposed faux pas

No, it isn't. Right this second, I could exit and tell ten Italians in ten different cities that you think there is a law/unwritten rule in Italy about eating while walking. Everybody would ask: "Eating while walking or camping?". Then they would all shrug, roll their eyes and say: "Americans...". In the same tone our cousins on the other side of the Alps say: "Ah! Les Italiens..."

Now you are all free to believe what you want about this matter. I'm done.