Having a cappuccino after a meal in Italy isn't considered sacrilege or barbarism or heresy or a crime, though you can be forgiven for sometimes getting an impression of that sort. No, it's simply un-Italian. The Italian reaction to this visceral affront can go from stoic forbearance to a furrowing of the brow, right to hyenic derision or a theatrical churning of the stomach.
Cappuccino here is generally considered a breakfast component, very often taken with a brioche – the now staple Italian breakfast – and most typically in a bar or cafe. Cappuccino can also be had as a snack in between meals, but never after one.
Simply put, ordering a cappuccino in a pizzeria is like yelling out for a bowl of breakfast cereal. You wouldn't do it. Would you?