Daveed Diggs, born poor and “very happy” in Oakland, California, says his Jewish mother and African-American father informed him early on that he was going to be policed differently than many of his friends. Regardless of the success he has had of late – including his double-star turn as both Marquis de Lafayette and Thomas Jefferson in Hamilton’s original Broadway cast - the 36-year-old says that fear is still “always there”. Growing up, he was never as aware of the imbalance as when he was around some of his more reckless white friends, a burden he compares to “a weight on my shoulders, a kind of disability that wasn’t shared by them”.

“I got pulled over the first time, five days after I got my driver’s licence, I was 16,” says Diggs. “My car was surrounded by four police cars, one of them walking up to the door with his hand on his gun. Because I had forgotten to turn my lights on and I was driving at night.” Over three years in his 20s, he was pulled over 36 times. “Two days before I left LA to move to New York to work on Hamilton, I got pulled off of my bike and thrown up against a fence by police officers who thought I fitted a description. These events keep happening. It doesn’t change. And so you live with it.”

This ever-present feeling – a sort of PTSD, he says, an awareness that your life is worth less than others – informs his new film Blindspotting, co-written by and starring Diggs and Rafael Casal. Blurring all comedy/drama boundaries, the film’s nuanced exploration of racial and class divides is set in the increasingly gentrified Oakland. Collin (Diggs) spends his final days on probation desperately trying to avoid trouble, not helped at all by his white, grills-wearing best friend Miles (Casal), or by witnessing a black man killed by a white cop.

Diggs exudes urgency as a traumatised man scrabbling to hold it all together. There is a vitality about him, which can also be heard on record with his rap group Clipping; he’s the same when in interview mode: always alert, switched on. At points in Blindspotting, Collin and Miles express themselves via spoken verse. It is intrinsic to the film and to Diggs who – long before Hamilton brought hip-hop showtunes to Broadway – battled in his school’s slam poetry competitions.

“When I started, it was a way to present my ideas in a way that people would listen to,” he says. “I was a poor black kid from east Oakland; nobody had any reason to listen to me. Historically, no one listened to me. But all of a sudden with this trick of making it sound pretty, everybody was not only hearing you but excited to hear what you were going to say next. That’s a very powerful thing for a kid to learn.”

Spoken verse gave birth to Blindspotting, but its journey from concept to fully formed film was a long and complex one. In 2007, Casal – then a twice National Youth Poetry Slam finalist champion – was contacted by film producer Jess Calder, who had seen him perform on YouTube and thought his talents could translate to film. In January 2009, Calder and her co-producer husband Keith screened Thunder Soul, their documentary about a high-school jazz and funk band, for the Congressional Black Caucus at Obama’s inauguration. They asked Casal to perform, but he couldn’t and recommended his best friend and collaborator Diggs, who was in Washington DC to soak up the presidential proceedings.

“Just off of seeing the movie, he freestyled for 20 minutes,” says Calder of Diggs. “Incredible, in-depth thematic content about the importance of music education and being able to save troubled youths all around the world.” Diggs had spent some of his 20s teaching rap to kids in school, helping them to find a voice. He was just paying it forward, he says. “He totally blew us away,” says Calder.

At the Tony awards in 2016. Photograph: Theo Wargo/Getty Images for Tony Awards Productions

The two producers asked Diggs to team with Casal: the film would capitalise on their chemistry, it would use verse, it would be about the Bay Area. That much they knew. But three weeks earlier, a 22-year-old, unarmed black man called Oscar Grant was fatally shot in the back by local police officer Johannes Mehserle at Oakland’s Fruitvale station, four blocks from Diggs’s apartment. “The town was furious,” he says. “It was caught on camera from so many different angles, because we all watched this boy murdered for no reason, and [the media and social media users] put that footage out there.

“It was an opportunity to show the whole world: ‘Look, this is real, don’t tell us we’re crazy, don’t tell us this doesn’t happen.’ We thought that everybody would see the same thing.”

Diggs hit the streets as part of the ensuing protests. And, as he and Casal began to write Blindspotting, such community action formed part of the plot. However, as time went on, that spirit began to seem out of step, not least because Mehserle was not convicted.

“It’s like, we didn’t all see the same thing,” says Diggs. “Not everybody saw what we thought was so clear – a black boy murdered for no reason,” he says. “These killings are happening fairly routinely these days. It feels like we don’t have that kind of capacity to riot and protest the way that we did back then [in 2009, in the aftermath of Grant’s killing], because that was based on a fantasy that everybody would look at the footage and see what we saw. And that’s not what happened. But that’s what Blindspotting ended up being about.”

By the beginning of 2015, the film was ready to go, but Diggs had landed his role in Hamilton. Creator Lin-Manuel Miranda had met him and invited him to an early reading of the musical because of his lightning delivery. It was after this major role that Diggs’s career soared and Blindspotting entered its lengthy limbo. After leaving the show in July 2016, Diggs, now armed with a Tony and a Grammy, got TV roles, in Black-ish, The Get Down and The Unbreakable Kimmy Schmidt, plus a part as an inspiring teacher in the Julia Roberts-Jacob Tremblay tearjerker Wonder.

However, the political pertinence of Blindspotting soon bubbled up again. Following Trump’s election in November 2016, says Calder, “a lot of people, and especially people of colour in America had a day of reckoning where you felt that everything you had been doing, you hadn’t been doing enough. I hadn’t yet made a movie that really commented deeply on what I felt was going on in our country.”

In Unbreakable Kimmy Schmidt with Ellie Kemper. Photograph: Eric Liebowitz/Netflix

Culturally, there was a shift taking place, too. Moonlight won the best picture Oscar, promoting Casal to text the Calders to say they might have their own Moonlight. “This little film’s success inspired us all to think: ‘Now is the moment,’” says Calder. Diggs had 22 days free, so they went for it, with director Carlos López Estrada, who had worked on various projects with Diggs and Casal, hired to direct.

Despite the delay, Blindspotting still seems particularly relevant. “We wish it was a period piece,” says Diggs. “It would have been nice to have it be a piece about 2009, but it’s just not the world we’re living in. Part of it has to do with our fucking insane neo-Nazi president occupying so much of the news space. We have someone we’re forced to look at all the time who is actively promoting so much hatred and breaking the law with impunity, and he is the leader of our country. So when you’re faced with that, the position that Collin is in becomes even more dire. You’re like: ‘Well there’s no way there’s any penalties for killing you.’” He laughs, macabrely.

While updating the script last year, it became clear to Casal what its title should be. “When you’re driving, you have to turn your head physically to see your blindspot,” explains Diggs. “You won’t see it by looking in your mirrors. It really is about the work that it requires. The film is advocating that right now we all need to be doing more work than we are when it comes to understanding the circumstances of people who aren’t us.” This extends to the use of the N-word, tackled head-on by Diggs and Casal in a climactic scene. Collin and Miles’s existences are different, explains Diggs of the interaction; the way the world is changing affects one differently to the other.

Oakland itself had been changing when they started writing the film in 2009, but gentrification has since transformed it. Oakland is 30% less black today than it was in 2000. Streets with bad reputations have been renamed. As in many cities, history has been erased. “The problem is not necessarily new business or new people, it is the intentional demolishing of the community that made the place attractive to begin with,” says Diggs. “And the lack of respect: to completely ignore what you moved in on top of, and asking all of a sudden for the culture of a place to bend to your way. BBQ Becky is my favourite example of that,” he says, citing the case this May when a white woman in Oakland called police to complain that some black people were using a charcoal grill in the park. “To call the police on a barbecue that’s been happening across the street from your house for decades is a crazy thing to do,” says Diggs, laughing heartily. “It’s actually insane. And also: are you aware as an older white person that calling the police on a gathering of people of colour may have different results than calling the police on you and your friends? The blindspots are endless. And they stack on top of each other.”

With Rafael Casal in Blindspotting. Photograph: Sundance Film Festival

Hamilton, of course, ended up being of great benefit to Blindspotting. “Any time I walk down the street with Diggs,” says Calder, “young kids run up to him who have listened to that soundtrack over and over again, and they hero-worship him.”

“Hamilton has totally changed my life,” agrees Diggs. “I was doing small theatre in the Bay Area and touring an experimental rap project. Those were my income streams. By the time I left Hamilton, I had already secured spots on Black-ish and Kimmy Schmidt, and the role in Wonder; this whole other world opened up.” He is currently on a seven-month shoot for the TV adaptation of Bong Joon-ho’s Snowpiercer, in which he’ll star alongside Jennifer Connelly. A feature film version of Hamilton is in the works, too (if “it’s a really good idea, I’m probably gonna do it”). Right now, Diggs wants to keep on doing everything.

“I approach everything the same way,” he says of his multi-pronged career. “The same way I approach writing, or rap, is the same way I approach developing a character when I’m acting. And for me and Raf, writing a script is like making songs. It’s all about keeping the energy of it. The goal is just to be able to support yourself doing the things that you love to do.”

Among it all, Blindspotting is what he is “most proud of”. And for all its dark subject matter, it ultimately concerns itself with human relations. For all its talking points, it never falls into polemic. It preaches not from a podium, but from the heart. It’s all about communication.