In fairness, a lot of Italian immigration happened at the time the peninsula was unifying under Garibaldi--so some of the mixing was happening in the old country! Ditto Germany. As far as I know, Mexico has been technically united all that time (nearly as long as the US) but it's not hard to imagine technological advance (both transport and media) serving much the same cause in Mexico as Nationalism in the previous waves.
Heck knows that's been happening here in the US!
Some of the mixing- in all three waves- was also the result of people from different parts of the old country settling in the same neighborhoods and working for the same employers. They not only had to unite against their respective know-nothing nemesi, they also had a chance to try aspects of each other's art, culture and cuisine to gradually for a mixture.