Radcliffe also said it was hard for gay actors to come out for fear of being typecast in gay roles.
And he stated that he did not want to play Potter again "at this point".
The 27-year-old British actor has starred as JK Rowling`s child wizard in several films since 2001.
But his latest screen role, in the thriller Imperium, is as Nate Foster, an FBI agent who goes undercover to infiltrate a white supremacist group.
`Fear and hatred`
Radcliffe told Victoria Derbyshire this had led him to think more about racial issues, and to consider how close to "mainstream" some of the opinions in the film had become.
He criticised the Republican US presidential candidate, Donald Trump, saying he had "stirred up" feelings of "fear and hatred".
The US film industry has itself come in for criticism for racism, with actor Dustin Hoffman and director Spike Lee boycotting this year`s Oscars ceremony over what has been described as a lack of ethnic minority nominees.
Asked whether Hollywood was "racist", Radcliffe, who is on the panel that chooses Oscar winners, said: "It`s pretty undeniable."
He added: "We like to think of ourselves as being a very, very progressive industry, but we have been lagging behind in all kinds of areas. "
Radcliffe also voiced concern that gay actors felt unable to come out because "I suppose then people just want to cast you as gay".
In 2012, the actor declared himself a supporter of the Labour Party, having previously backed the Liberal Democrats, and has since voiced support for leader Jeremy Corbyn.
Asked about recent allegations of anti-Semitism within Labour, Radcliffe - whose mother is Jewish - described them as "absolutely awful" and "shocking".
But he said he was still likely to back Labour at the next election "if it was a choice between that and the Conservatives".
There has been speculation that the London stage play Harry Potter and the Cursed Child could be turned into a film, starring Radcliffe.
But he said: "No-one`s asked me about it and I definitely don`t think that I would do it at this point, certainly.
"It`s only been six years [since last playing Potter] and I`m really enjoying being able to do lots of different stuff at the moment."
He added: "Maybe if 30 years had passed I would be thinking differently. They will be doing remakes, and I could play his dad, or something."
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