But the critics have stepped up their attacks, with one accusing the festival of “almost comically scant levels of self-awareness”.

“1 rapist. 2 women directors in competition at Venice. What else am I missing?” tweeted Women and Hollywood founder Melissa Silverstein, referring to Polanski’s conviction for the statutory rape of a 13-year-old in 1978.

She was equally scathing about the late addition of American director Parker’s film American Skin to a sidebar section of the festival.

“Good job Venice,” she tweeted caustically, adding a reference to a rape trial the actor-turned-director was embroiled in while still at university.

Although Parker was acquitted, he later admitted: “I look back on that time as a teenager and can say without hesitation that I should have used more wisdom.”

Fellow black American director Spike Lee has vowed to travel to Venice to support Parker.

“I haven’t been affected by a film like this … in a long, long time,” he said in a statement about Parker’s film, in which a US Marines veteran whose son is killed by the police takes justice into his own hands.

But it is the premiere of 85-year-old Polanski’s historical thriller about the persecution of the French Jewish army officer Alfred Dreyfus, An Officer and a Spy, which is likely to make most headlines.

The Polish-born director jumped bail in 1978 as he awaited sentencing for unlawful sexual intercourse with a 14-year-old girl; charges including rape were dropped under a plea bargain. With Polanski suing the Academy of Motion Pictures for stripping him of his membership, Screen Daily’s chief critic, Fionnuala Halligan, was withering about his selection.

She imagined festival director “Barbera, wandering the Lido hopelessly, singing the same mournful refrain … he can’t find a female film director.

“So this year he’s going to programme the new film by [a] convicted child rapist.”

The message was “crystal clear”, she added: “You don’t cut it, ladies.”

Halligan wrote that such “gender imbalance … shouldn’t be acceptable and Polanski is just like rubbing salt into that.”

She also deplored the decision to add the director’s cut of French director Gasper Noë’s controversial 2002 rape shocker Irreversible to the festival line-up.

“Time to turn over,” she argued.

Barbera defended his selections, insisting that “numerous films this year deal with the theme of the feminine condition in the world which, even when directed by men, reveal a new sensitivity”.

He said this was “proof that the scandals of recent years have left their mark on our culture”.

The rows threaten to take some of the sheen off a staggeringly starry selection that features Brad Pitt, Johnny Depp, Kristen Stewart, Meryl Streep, Scarlett Johansson and Mick Jagger.

Adam Driver, Penelope Cruz and Robert De Niro are also due on the red carpet.

The curtain will also come up in Venice on the new DC Comics blockbuster, The Joker. Trailers for the film, starring Joaquin Phoenix, which traces the origins of Batman’s nemesis, have already been viewed more than 80 million times.

Steven Soderbergh’s take on the Panama Papers investigation, The Laundromat, will also be premiered, while Pitt plays an astronaut in James Gray’s highly anticipated sci-fi drama Ad Astra.

Japan’s Hirokazu Koreeda – who won best film at Cannes last year with Shoplifters – opens the festival with his French-set family story The Truth, starring Catherine Deneuve, Juliette Binoche and Ethan Hawke.

The two female directors vying for the top prize are Saudi Arabia’s Haifaa al-Mansour, the maker of the acclaimed Wadjda, with The Perfect Candidate, and newcomer Shannon Murphy, for the Australian comedy Babyteeth.