Juventus is both the most popular and the most disliked club in Italy by far. The support that Juventus has in Italy is far greater than any English club has in England, even compared to United. Even Bayern doesn't have that level of support in Germany.
The popularity of Juventus across Italy is due to several reasons. Number one is obviously the historic success of the club. But another important fact is that Juventus always had a strong Italian core of players and provided many players for the most successful Italian national teams in history. 2006 being the prime example in recent history, with the heroics of Buffon, Cannavaro and Del Piero on that tournament. So a lot of people love Juve as the symbol of Italian football and Italy as such, a bit like Ferrari in Formula One. There's also the FIAT connection, with Juventus being the club of FIAT workers. This is especially true for southern Italians who worked at FIAT factories and didn't have a club of their own to support (outside of Napoli the south of Italy doesn't really have a strong club, and many people there don't like Naples). So Juventus has a huge fanbase in southern Italy and Sicily as a result.
But for the people who hate Juventus, Juve is annoying because pretty much anywhere you are in Italy and whatever team you support, the chances are you'd encounter Juve fans all the time and they'd gloat over beating you and celebrate winning titles. Juve is sometimes mockingly referred to as the "second team" in every city in Italy, as Torino fans like to claim that they are more numerous in Torino itself which I don't think it's necessarily true, but the number of fans of these two clubs in Torino is definitely much closer than it should have been based on historic success. Juve is also seen as a bit of a rootless club that doesn't have a strong connection with local community and represents "modern football", capitalism and globalism. For the likes of Napoli fans and fans of other soutnern Italian clubs, Juve is also seen as the representative of everything they hate about the northern Italy. Then there's obviously the cheating controversies, namely the Calciopoli affair and various doping allegations. Juventus built its identity on being this ruthless club that does anything to win, reflected by its unofficial motto "winning isn't important, it's the only thing that matters."
For these reasons, the hate Juve gets in Italy is even greater than the hate United, Real Madrid and Bayern get in their own countries.
As for Inter, they're quite hated over Italy as well. Some of it is down to similar reasons as Inter (a successful wealthy team from the north). But Inter fans are also seen as elitist and smug, they have this attitude that they're morally superior to Juve, especially after the Calciopoli, but for fans who hate them they're basically just seen as another Juve and hypocrites. However it doesn't come close to the hate Juve get.
I think there are several other clubs in Italy that get similar level of hate as Inter across the country. Lazio is definitely a candidate for the second most hated club in Italy because of its reputation for being a "fascist club" due to having a large group of violent neo-fascist ultras (who are also tied with organized crime and are seen as thugs). Lazio fans are also seen as similarly elitist as Inter fans. They actually pride themselves in having less fans in Rome than their city rivals Roma, as they see being a Lazio fan as an exclusive thing. They're also very tribal as a result, as they're used to being outnumbered in their own city, where Roma fans are the massive majority. I remember talking to a Lazio fan and he told me that going to a high school, it was not uncommon that Lazio fans were so few in their own city that you would be nicknamed "the Lazio fan" if you were one, because it was so rare. This was before Lazio had their big success in the 90s when they picked up some more fans, but still lag behind Roma. Also this period of success was seen as "bought" by others, due to Cragnotti investing huge money (for the time) in the team and buying marquee players. Lazio fans are allied with Inter fans too so this doesn't do either of them any favors in the eyes of people who hate either of these two clubs.
Roma is hated in every part of Italy for being the representative of the capital. Romans are hated both in the north and in the south, as the city is associated with corruption and like in many other European countries, nobody really likes the capital city. The hate that the rest of Italy has for Rome actually goes back even further, before Italy even existed as a country, as Rome was the seat of the Papacy and the city was often a violent and corrupt mess due to rival noble families fighting for control of the papacy and of the city. This is in contrast to for example the prosperous and well-organized cities in the north which flourished in middle ages and renaissance like Venice, Milan, Genoa and Florence. So people from north always looked down on Rome as being a corrupt backward city that tries to live on its long gone glory of antiquity, and this tradition can still be seen today and reflects in the hate Roma get as football club. Roma has fierce rivalries with the likes of Napoli and Atalanta, as both of these fans are very passionate and absolutely hate Roma and Rome. So despite not being nearly as successful as the big 3 of the Italian football, Roma is hated all over Italy similarly to Inter.
I have to also mention Verona which is a club that gets disproportionate ammount of hate for the level of where they are at as a club, as they're basically the Millwall of Italy. Their fanbase is seen as racist, fascist and extremely hateful. Their ultras are openly fascist and have had numerous racist and other controversial incidents over the years. The city of Verona is also stereotypically seen as a bastion of far-right and xenophobia. Veronese fans have been especially hateful towards southern Italians, which is related to the rivalry they have with Napoli as both of these clubs had their golden years in the 80s when they were both title contenders for a short period (Verona actually won a title in 1985 in a Leicester-like story and had another title challenge in 1987 when Napoli won it). When they played in Verona, the home fans insulted Napoli fans with banners like "Welcome to Italy", "wash yourself" etc. The Napoli fans responded by insulting the very core of identity of Verona as a city by calling Romeo gay and Juliet a whore. Ever since there has been a bitter hatred between Verona and Napoli which also transferred to other southern Italian clubs hating on Verona. It doesn't help that the Veronese ultras openly accept the negative image people have of them, flying banners like "we hate everyone". Them booing Ibrahimović farewell speech in Milan for no other reason than being spiteful and trolling is stereotypical Verona fan behavior. Like I said, basically the Millwall of Italy.
Napoli is hated all over Italy because of the negative image people have of the city due to organized crime and garbage issues. They're also by far the biggest team of the south and nothern Italians who hate the southerners focus their hate on Napoli. But they're not universally loved in the south either, as they have local rivalries with other southern clubs.
Milan also gets hate all over the country because of similar reasons as Inter and Juve, but is still less hated than Inter and definitely much less hated than Juve.
To sum it up, Juventus are the most hated club in Italy. There's a huge gap between them and the rest in terms of hatred they get. Then there's a second tier of hated clubs which includes Inter, Lazio, Roma, Verona and Napoli. Atalanta and Fiorentina also annoy a lot of people but I don't think they really get nation-wide hate.
