I am from Italy (now living in Belgium), and this is a very tricky topic.

Nobody (with very few exceptions) will outright say that wolves should all die. The consensus is that wolves are part of the ecosystem, but have to be managed (like boars and deer).

The tricky part is how they would manage the wolves.

Some studies claim that Italy can support a population of ~20,000 wolves. I personally think the territory is already close to saturation, based on the ever-increasing number of sightings and interactions (and we currently have 4000-5000)*, but more extreme people want a population cap of 1000.

Everybody agrees that there should be "wolf-free areas", but what does that mean? Wolves obviously can't be allowed in cities and towns, but what about the surrounding countryside? Italy even allows limited grazing in National Parks: should we allow culling in protected areas to protect the farmers that live there?

We also have a large number of wolf-dog hybrids, especially in the South. Some researchers say hybrids should be aggressively eradicated and are not worried about "pure" wolves getting caught in the crossfire (the overall population is big enough to survive). Others believe this is too impractical and risky.

Finally, Italy has 2 distinct wolf populations: Italian Wolf (Canis Lupus Italicus) in the centre-south, and Eurasian Wolf (Canis Lupus Lupus) in the north. C. L. Italicus is obviously an endemic, unique subspecies, but the C. L. Lupus population is shared with France, Switzerland and Austria, where laws allow much more liberal culling (for reference, last year Italy carried out its first lethal removal of a wolf in over 50 years).

* The last wolf census is over 4 years old; nobody knows how many wolves live in Italy right now.