Could it be the Italians had the gall to snub history or other foobar ideology and chose to hoist a flag that represents their most common ingredients used in their dishes?

No, no and no. In short (I'm on mobile!) the flag was actually created after Napoleon's 1796 invasion of Northern Italy, who then proceeded to establish a number of "sister republics" in lieu of the old states. The kind of flag the representatives of these republics had chosen was perhaps unsurprisingly modelled upon the French one, with green - due to it being the colour of Milan's civil guard - taking the place of blue. With the proclamation of the Napoleonic Kingdom of Italy (1805-14) a slightly modified version of the flag was adopted but despite it having a different shape now, its three colours had become a symbol for the Italian patriots and they stuck to them even after Napoleon's defeat.

By 1848 the flag as we know it today - defaced with the crest of the House of Savoy, something that was only eliminated in 1946 - had been adopted by Sardinia-Piedmont, that is, the state which would later unite Italy.

As an unrelated curiosity, the Italian flag doesn't have anything to do with food whatsoever and the ingredients you were probably thinking of (tomato, mozzarella, basil) are actually prevalent in the Southern Italian cuisine; these don't therefore represent the lots of other regional cuisines which mostly make use of other things.

and while we are here .. why blue for their sports?

This is because the colour in question is blu Savoia (a particular shade of blue that had become associated with Italy's Royal Family because of a number of historical vicissitudes). But this wasn't always the case; prior to 1912 the Italian football team sported white kits and during Fascism these were actually black.