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The Los Angeles collective was meant to be playing at the Rapture hip-hop festival in Auckland tomorrow but was refused entry after being determined a threat to public order.
It was to be an emergency replacement after Kendrick Lamar - one of the show's top billings - announced he was pulling out because of an "unavoidable scheduling conflict".
However, in a statement this week Immigration New Zealand said Odd Future had been deemed a potential threat to public order.
Border operations manager Karen Urwin said authorities decided to decline visas to six group members after becoming aware of a 2011 incident in Boston in which some witnesses claimed group members incited fans to attack police officers.
In that incident, at an album signing for frontman Tyler, The Creator, the group climbed on top of the shop and ran from roof to roof. A police officer was hurt and a 13-year-old girl arrested.
Immigration NZ's decision came days after sexual violence advocacy group Stop Demand emailed Auckland councillors, criticising the decision to allow the group to perform at the Western Springs event.
The email quoted several lyrics from Odd Future which referred to rape.
Stop Demand founder Denise Ritchie said the organisation had been inundated with hate mail since the decision was made public.
"Our Facebook page, I was told by a volunteer of our organisation not to go into it because it was too vile...it included a rape threat against me, a death threat and, I'm not sure if it's still up, but a threat to burn my house down."
She described the decision to block members of the group from New Zealand as great, and said the organisation was aware that the reason was not because of the group's lyrics.
Stop Demand had targeted Odd Future and not the equally controversial headline act Eminem because it had to pick its battles, Ms Ritchie said.
Prime Minister John Key weighed in yesterday, saying that while Immigration NZ would have had its reasons for cancelling the visas, it would have been better if the decision had not been last minute.
"There will be plenty of people who go to the concert who will be feeling quite frustrated by that. I ran into a few of them when I was coming off the plane arriving in Wellington [yesterday]. People are frustrated."
He said Immigration NZ operated at arms' length from the Government. "I'm sure they had their reasons. It's good if they can communicate that early so the fans know."
He had not known about it until he saw it on the news. "I know very little about their music apart from apparently a lot of their lyrics are extremely provocative."
New Zealand rapper David Dallas, who is also playing at Rapture, vented his frustration at the decision, via Twitter, saying: "NZ Immigration looking very Draconian.".
Odd Future were last here in 2012. They were set to perform at the Big Day Out, but had their performance axed after complaints their homophobic lyrics encouraged bullying and violence.
They denied they were homophobic, came anyway and performed an incendiary sideshow at Auckland's Powerstation the night before the Big Day Out.
- By APNZ and Hew Zealand Herald staff