Writer-director Spike Lee showcases the full range of his impressive versatility in “BlacKkKlansman,” a story so improbable it had to be based on real-life events and a film that could just as accurately have been titled “Code-Switching: The Movie.”

Based on the 2014 memoir “Black Klansman” by retired police officer Ron Stallworth, Lee’s film casts John David Washington (equally talented son of Denzel) as Stallworth, who not only became the first African-American police officer in Colorado Springs in the 1970s, but also successfully infiltrated the Ku Klux Klan, just as David Duke had ascended to leadership of the notorious hate group.

We see Stallworth team up with his Jewish fellow undercover police officer, Flip Zimmerman (played by Adam Driver), with Stallworth making and maintaining contact with members of the KKK on the phone, pretending to be a racist white man who wanted to join them, while Zimmerman played “Stallworth” when he needed to meet those same KKK members in person.

While both the black Stallworth and the Jewish Zimmerman are shown coping with the challenges of portraying themselves, jointly as this fictional white racist, also named “Ron Stallworth,” through the course of his screening and recruitment by the KKK, we see both men are also struggling to reconcile dual identities in their personal lives.

During his first stint as an undercover officer, attending a rally by black civil rights leader Kwame Ture (born Stokely Carmichael), Stallworth strikes up a romantic relationship with Patrice Dumas (played by Laura Harrier), the president of the black student union at Colorado College.

Patrice challenges Stallworth’s belief that he can support the liberation of his fellow black people while still serving as a police officer, a belief that’s already difficult for him to maintain in the face of blatant yet casual racism from his fellow police officers.

Thanks to Patrice’s scholarly studies, Lee is able to embrace civil rights activist W.E.B. Du Bois’ ideas of the “double consciousness” of African-Americans, as being both American and black, during the course of her conversations with Stallworth, even as they also debate the cinematic and cultural merits of “Shaft” versus “Super Fly.”

At the same time, Stallworth calls out the Jewish Zimmerman for “passing” as a WASP, causing Zimmerman to finally reflect on the Jewish heritage he was born with but was never really enculturated into as he was growing up.

Just as we see the black Stallworth impersonate the white “Stallworth” by alternating between, as he refers to it, “the King’s English and jive” in his spoken language, so too does Lee execute a deftly orchestrated composition of code-switching as a filmmaker, interweaving laugh-out-loud moments of bizarre absurdity with haunting reminders of the power and horrors of racism.

You don’t cast Topher Grace as David Duke unless you intend to fully acknowledge the inherent ridiculousness of the Ku Klux Klan and the wrongheaded people who subscribe to its cause, but Lee never lets us forget that such fools, whose flaws can often seem comic, are nonetheless deadly serious in the threat they pose.

Perhaps Lee’s best sequence features Grace as Duke, delivering a genteel speech to his fellow Klansmen, full of mealy-mouthed yet dog-whistle-laden platitudes that sound disturbingly similar to any number of modern political speeches.

The film is repeatedly intercut with the recollections of Harry Belafonte, playing a fictional character who was witness to the all-too-real 1916 lynching of Jesse Washington in Waco, Texas.

Belafonte’s in-character remarks are lent an affecting gravitas and fragility by his advancing age, as he quietly recounts how Jesse Washington was gruesomely dismembered and burned, in public view of more than 10,000 spectators.

Just as Belafonte’s character attributes much of the mob’s racial frenzy to a local screening of D.W. Griffith’s “The Birth of a Nation,” which was originally released in 1915, one year prior to their act of lynching, so too are we shown Duke and his fellow Klansmen cheering on the KKK’s acts of terrorism against blacks, as they watch “The Birth of a Nation” in Colorado Springs in the 1970s.

Lee allows us moments to laugh at the expense of these racists’ buffoonery, such as when Duke personally expedites Stallworth’s KKK membership process during a phone conversation, after identifying the black undercover officer as a fellow “true white American” — and yes, that actually happened — but it’s only so he can sucker-punch us by drawing a straight line between Duke’s attempts to “mainstream” the KKK and the recent resurgence of unabashed demonstrations of racism.