(Update: According to a spokesman for Arena Stage, Robert Jimenez withdrew Friday from “Celia and Fidel” for personal reasons. He is being replaced by Andhy Mendez. As a result, the first four preview performances have been canceled. The play will now begin March 3.)

To take on any role, an actor prepares. But for the role of a real-life character whose very name can be an incitement, an actor really has to be prepared.

This article of artistic faith has been inculcated by not one but two actors on Washington stages these days, performers embodying polarizing figures whose entrances might best be accompanied by trigger warnings. At Woolly Mammoth Theatre, it is Jeff Biehl who has waded into these choppy waters, portraying Donald Trump in Anne Washburn’s new play, “Shipwreck.” On the Southwest Waterfront, meanwhile, Robert Jimenez is ensconced at Arena Stage as the late Cuban president-for-life Fidel Castro, in the world premiere of Eduardo Machado’s “Celia and Fidel.”

Audiences seem to have a limitless appetite for global newsmakers in modern plays, and they pop up again and again: at Arena, Jimmy Carter in “Camp David” and Supreme Court Justice Antonin Scalia in “The Originalist,” and on Broadway, onetime Israeli president Shimon Peres and PLO chairman Yasser Arafat in “Oslo”; Lyndon B. Johnson, in “All the Way”; and Bill and Hillary Clinton and Barack Obama in “Hillary and Clinton.”

They’re lightning rods by virtue of hot personalities, or the hot seats they’ve occupied, or both. But few figures can inflame passions quite like Trump and Castro. Because of the powerful emotions playgoers harbor about these men, Biehl and Jimenez say the roles are like none they have ever undertaken. As Biehl described his peculiar situation: “I’m sitting reading the scenes when I’m playing Trump, and he’s on CNN being impeached.”

Or, as Jimenez mused about the potential reaction of theatergoers with a personal history with Cuba: “I’m worried about people from an older generation saying, ‘Damn it, how dare you do Fidel!’ But we’re not minimizing or endorsing his point of view. This is a historical figure in the setting of a play.”

In “Shipwreck,” a work intermingling the country’s liberal political arguments with the story of a young black man coming to terms with his identity, Trump is quite literally a side show. While a dinner gathering of political liberals agonizes over the state of the nation, he appears, amusingly, in a pair of scenes: one a flashback to an imagined conversation with then-President George W. Bush over Trump’s position on the Iraq War, and the other a kind of satanic re-creation of a meal between Trump and the FBI director he would soon fire, James B. Comey.

“My head was filled with all of this political language. I was obsessed,” said playwright Washburn. “Shipwreck” was an attempt by Washburn, who wrote another extravagantly inventive Woolly play, “Mr. Burns, a Post-Electric Play,” to wrestle with the language of cable news chatter and to find a vehicle for an alternate vision of Trump: the Trump, perhaps, that Trump himself sees.

“I think of that being Trump’s idealization of himself,” Washburn said of the risible scene she concocts, in which Trump discusses global matters with Bush as if the former were some amalgam of an august industrialist and senior fellow at a foreign-policy think tank.

“To us, it’s an absurd scene,” she added. “But to a certain Trump supporter, that is the person they’re imagining.”

The bearded, follically challenged Biehl would not exactly be thought of as a double for Trump; neither is Jimenez a physical match for the swaggering, cigar-smoking Castro of the popular imagination. Impersonation isn’t what either of these plays is after, even if “Celia and Fidel” was inspired by the real relationship between Castro and Celia Sánchez, his close adviser and fellow revolutionary.

That Washburn and director Saheem Ali didn’t expect Biehl to be either a Madame Tussauds-style waxwork or a buffoonish caricature a la Alec Baldwin on “Saturday Night Live” came as a relief.

“Oh, my God,” Biehl recalled initially thinking, “am I going to have to go down a Trump wormhole of videos and more videos?” Rather, he said, illuminating the president in unexpected shades is somehow even more useful.

“I think there’s something about the way he’s projected in the play, that it’s not a direct impersonation, that it’s a different kind of imagining of him, ends up maybe being more revealing of him,” Biehl said. In other words, what’s dramatically interesting is how theatergoers’ perceptions are affected when presented with a fantasy version.

For Jimenez, whose parents were born in the Dominican Republic and who had a Cuban grandfather, becoming Fidel entailed more historical digging. The play revolves around events in 1980, when the Castro regime faced economic disaster and thousands of Cubans tried to flee the country.

“[Director] Molly [Smith] and her staff have been wonderful about bringing in learned professors — PhDs who were focused on politics and geopolitical actions, someone who is familiar with the Carter years,” the actor said. A Georgetown University professor, Soyica Colbert, chairwoman of the performing arts department, has sat in on rehearsals, too.

The process also dug up some personal associations for Jimenez. Having grown up in New York City with a Republican father fiercely proud of his military service, the actor tended to hear a dissenting voice in his head as he tried to assimilate Castro’s Marxist dogma. It has been a complex balancing act: He has had to absorb a character and a playwright’s words while remaining mindful of the people — even some in his own life — who may resist any humanizing of a man they regard as brutal and a dictator.

But still, one wonders: Is it enjoyable for these actors, viewing these characters from the inside?

“Well, in his mind, it’s pretty great to be him,” Biehl said of Trump. “And it is tremendous fun to be so powerful, and ­certain.”

Shipwreck, by Anne Washburn. Directed by Saheem Ali. Through March 8 at Woolly Mammoth Theatre, 641 D St. NW. 202-393-3939. woollymammoth.net.

Celia and Fidel, by Eduardo Machado. Directed by Molly Smith. March 3-April 12 at Arena Stage, 1101 Sixth St. SW. 202-488-3300. arenastage.org.