White words on black walls: a ring of names, places and dates run around the room like a watermark, like limescale. They're not all familiar, but you know exactly what they represent: Trevon Johnson, 17, Miami; Sandra Bland, 28, Texas; Freddie Gray, 25, Baltimore. These are America's dead, the young black men and women killed by police over decades. The most recent are stark, others have faded to grey. The number of them is astounding. It turns the theatre into a crypt.

It's fitting. Tearrance Arvelle Chisholm's family drama asks us to reflect on the right response to the realities of racism in America today: police shootings, alt-right trolls and all manner of ingrained structural inequalities. It pits rage against resignation, rising up against getting on, and Chisholm's all too aware that there's no single right answer. The issue's intractable; the play's almost unbearable.

Br'er Cotton sits three generations side-by-side. Fourteen year-old Ruffrino swaggers downstairs in Black Panther-style beret. In his backpack, lighter fluid and a handaxe to "wake up the zombies" at school with a protest. His grandfather Matthew (Trevor A Toussaint), huddled in his beige dressing gown, takes a more sanguine approach: "I just think each generation ought to do a little bit better than the one before."

But what counts as progress when black men are still being shot in the streets? Ruffrino's mother Nadine (his estranged father's in jail) cleans the houses of white families for minimum wage – still a maid, albeit paid. She snatches quiet moments on the job to study for a nursing diploma, but her betterment is born out of uphill struggle. Sam Cooke's velvety voice bleeds out of her headphones: "A Change Is Gonna Come." Br'er Cotton is nothing if not sceptical: "If so," it demands, "when?"

Throughout, the past bubbles up like backwash: retro revolutionaries, slave soldiers, cotton plants climbing the walls. Jemima Robinson's surrealist design tangles a tree up in rope, tying today's shootings to the lynchings of old. But it's also an acutely contemporary play that swerves off into virtual worlds. Ruffrino spends his days playing an online shooter that's both riddled with racist trolls hunting down black players and a safe space to swap ideas about race and resistance. It cuts to the core of a generation's entrenched attitude – why Ruffrino sees his grandfather as spineless; why he "f**king hates white people"; why he wants a fairer, freer world now.

But Chisholm's too careful to let that go uncritiqued. Without ever letting white America off the hook, he counters Ruffrino's absolutism with two extraordinary encounters: Nadine's kindly employer, a white police officer, and Ruffrino's online playmate Caged_Bird99, a disabled white woman with whom he finds a kind of kinship.

It adds up to an intricate consideration of the complexities of present-tense race relations, but Roy Alexander Weise's production ensures it's always fully-felt. Michael Ajao is superb as the hot-headed, soft-hearted teenage revolutionary, his swagger suggesting an air of adopted certainty, while Kiza Deen, quietly heartbreaking as his mother, is beautifully matched by Alexander Campbell's caring cop.

But it's the force of argument that really affects. This damning indictment of rising racism is never less than sympathetic, recognising that keeping your head down is no more a failure than rising up is a responsibility. Either way though, the problem persists.

Br'er Cotton runs at Theatre503 until 31 March.