The “hoi polloi” are much more concerned about dictatorial Eurocrats interfering with the results of a free and fair election. Italy’s immigration problems are not the size of those in France nor Germany.
What has them enormously irritated is that the Italian President, who is a EU true believer, is putting EU interests first, and denying the electoral winners the government of their choice.
I personally think has backfired, and the chance of an Italian exit from the EU is a lot more likely than it was a couple of weeks ago.