Shiv Sena supporters tear a poster for Shahrukh Khan's new film My Name Is Khan. Photograph: Amit Dave/Reuters

A few days ago, the biggest movie star in the world remarked that the Indian Premier League could show "a little more leeway" when no Pakistani players were selected for the upcoming Twenty20 cricket competition. Then all hell broke loose, and it has yet to be recaged.

As of today, more than 1,800 people have been arrested in Mumbai for vandalising cinemas advertising Shahrukh Khan's latest movie, My Name Is Khan. This weekend, 21,000 special police will protect cinemagoers, and there will be security checks at the box office. "This is not Shahrukh, but the Khan in him that's saying all this", said a spokesman for the Shiv Sena, the militant Hindu nationalist organisation in Maharashtra which is behind the trouble. The Sena told Khan – an Indian Muslim – to move to Pakistan, and issued a threat: "There will be dire consequences if Shahrukh defies the orders of the Sena chief."

The film itself has not provoked the fuss, though its title, a declaration of Islamic identity, does resonate. It's a honey-coated melodrama about an autistic Indian Muslim man finding love in California after 9/11. If that sounds singular, just wait for the second half, in which George W Bush stands idly by while the desi hero singlehandedly saves a community of African-Americans after a Katrina-style hurricane. Several screens in Maharashtra have already pulled My Name Is Khan. Too bad for audiences, who will miss the remarkable scene in which Khan wins the hearts of the aforementioned African-Americans by expressing to them in passionate Hindi his love of Manchester United.

But there's nothing funny about the Sena's threats. "The Shiv Sena is one of the most extreme faces of Hindu nationalism," says Edna Fernandes, whose book Holy Warriors explores religious fundamentalism in India. "Its leader, Bal Thackeray, is like a godfather. His modus operandi is to whip his people up to a frenzy, and then it's up to them what they do. He can be charming in person, but at the other end of the line you've got people getting murdered in Muslim communities. It's not a joke."

Going after celebrities, says Fernandes, is part of the Sena pattern. In the past, its targets have included artist MF Husain and cricketer Sachin Tendulkar. Husain's studio was ransacked, as was a television station that defended Tendulkar. Several of the station's staff were beaten up. In 2008, a Sena splinter organisation, the MNS, pilloried Jaya Bachchan, wife of veteran Bollywood A-lister Amitabh Bachchan, for speaking a few words in Hindi rather than Marathi at a film premiere.

Indian celebrities, including the Bachchans, have often caved under such pressure. So far, Khan has not. He continues to put forward a moderate line, with a dignity you might not expect from a 44-year-old man whose career consists largely of dressing up in tight trousers and miming to someone else's vocals. Fellow megastar Aamir Khan, whose recent film 3 Idiots smashed multiple box-office records, has stepped in to support him. The Sena termed both men the "2 Idiots", and its supporters burnt them in effigy.

"A large section of India finds the Sena repugnant," says Fernandes. "India wants to see itself as a modern economic power. These communal conflicts are hugely damaging to that." If Khan surrenders today, the Sena will find another example of free speech and tolerance to besiege tomorrow. The message of My Name Is Khan is that extremism must be challenged. This weekend, we will see whether Bollywood's reality lives up to its talk.