Captain Fantastic,” starring Viggo Mortensen as a shaggy father of five who has raised his children off the grid, in the deep forests of the Pacific Northwest, is an independent movie that’s at once original and softheaded, tough and sentimental, honest and manipulative. It’s far from great, but it’s highly worth seeing, and the secret weapon of why it’s been connecting with audiences is that it’s the rare movie that can truly be called left-wing and right-wing at the same time. It’s a blue-state-meets-red-state domestic wild-woods fantasia that swings in both directions at once, and that isn’t a matter of dramatic confusion. It’s a matter of how well the film channels the confusions of our time.

We’re living at a moment, after all, when Donald Trump is on the right, Bernie Sanders is on the left, and Hillary Clinton is at the center — but the supporters of Trump and Sanders have more in common, in many ways, than either faction has with the supporters of Clinton. The left and the right in America are now selling different versions of anti-establishment fervor, and “Captain Fantastic” doesn’t just reflect those two poles; it fuses them. It taps the topsy-turvy sympathies that now rule the political-cultural zeitgeist. The movie, however, isn’t necessarily out to do any of that. It’s just trying to tell a story that might be described as “The Swiss Family Robinson” meets “The Wolfpack.” Here’s a breakdown of the intriguing, and largely unintentional, ways that “Captain Fantastic” is left-wing and right-wing at the same time:

Left-wing: The Mortensen character, Ben Cash, is a latter-day hippie with a beatific stare who has organized his family into an idyllic commune. Everybody shares everything, everyone is really nice to each other, and life in the woods looks like an episode of “The Brady Bunch” as scripted by Henry David Thoreau.

Right-wing: Ben may be a long-haired idealist, but he is also a tooth-and-claw survivalist whose hostility to anything resembling civilization places him somewhere between Grizzly Adams and the Unabomber.

Right-wing: Ben and his family are hunters, and he has trained his children to kill animals with a variety of weapons, including eight-inch Bowie knives, which he favors as birthday presents. He tells them to “keep your eyes open for game of any kind.” At times, it feels like we’re watching deer-skinning outtakes from “The Ted Nugent Story.”

Left-wing: The Cash family eat everything that they kill, thus preserving the cycle of ecological harmony. They also eat a lot of plants.

Left-wing: Outdoing the celebrity fetish for naming kids things like Blue Ivy and Apple, Ben and his wife have given their children made-up names like Vespyr, Zaja, and Rellian. That’s so each of them will have a name shared by no one else in the world — a celebration of their individuality that makes each of them sound like a character from a medieval videogame.

Right-wing: Ben’s 12-year-old son, Rellian (played by the scene-stealing Nicholas Hamilton), is moved to rebel against his father because he truly resents being named “Rellian.” And with good reason: No child on the planet should be named Rellian.

Left-wing: Ben’s children, who are home-schooled, have read — and, apparently, understood — every nuance of every book from “The Brothers Karamazov” to “Middlemarch” to “Lolita,” making them walking repositories of humane enlightenment. They’re the liberal-arts equivalent of the Von Trapp Family Singers.

Right-wing: They’re such extraordinary students because Ben is a rigorously demanding teacher, a stern advocate of traditional study who questions them like the headmaster of a Jesuit academy.

Left-wing: The reason that Ben first moved his family into the woods is that his wife suffered from bipolar affective disorder. The two thought that being out in nature, away from the evils of society, would cure her mental imbalance. The film pings off the philosophies of R.D. Laing, the ’70s countercultural psychiatrist who theorized that mental illness — in particular, schizophrenia — was the product of a repressive society.

Right-wing: The 1970s nature cure didn’t take. Early on, we learn that Ben’s wife, after deteriorating and being placed in a hospital, committed suicide. It was Ben’s hippie purity that probably killed her, whereas an openness to the remedies offered by Big Pharma could possibly have saved her life.

Left-wing: To attend the funeral, Ben and his family travel to San Diego in a souped-up school bus befitting the Merry Pranksters or maybe the Partridge Family.

Right-wing: To launch their journey, Ben blasts music from a speaker mounted on the bus. When he flips the switch, you’re certain that it’s going to be some classic nugget of rock & roll freedom, but instead it’s a Scottish bagpipe call to arms, less “Born to Be Wild” than “Braveheart.”

Left-wing: Ben’s philosophy is summed up by the credo “The powerful control the lives of the powerless.” Very Bernie Sanders.

Right-wing: Ben’s philosophy is summed up by the credo “The powerful control the lives of the powerless.” Very Donald Trump.

Left-wing: At a supermarket, Ben leads his kids in a cleverly orchestrated act of shoplifting. The film’s implication is that they’re anarchic “freegans” who aren’t even stealing, they’re just taking what The Man already took from them.

Right-wing: At a supermarket, Ben leads his kids in a cleverly orchestrated act of shoplifting. The other implication is that he’s inviting them to act like reckless junior-league sociopaths.

Left-wing: Ben hates organized religion, and he has come up with a holiday that the Cash family celebrates in place of Christmas. It’s called Noam Chomsky Day, in honor of the patron saint of muckraking leftist-analytical insight.

Right-wing: Rellian, who despises Noam Chomsky Day, openly wishes that the family could celebrate Christmas, thus putting him in league with all those talking heads on Fox News who angrily stand up for the right of sales clerks to say “Merry Christmas.”

Left-wing: At the funeral, Ben and his kids burst into the church looking like refugees from a homeless road-company production of “Godspell.” Ben then stands in front of the casket and reads his wife’s will, which decrees that she wants to be cremated — a speech that makes her straitlaced, overly controlling father, sitting there in his pew, glower with conservative outrage.

Right-wing: The father, Jack, is played by Frank Langella, an actor of such towering humanity that he couldn’t play a caricatured right-wing lout if he tried. In a lesser movie, Jack would have been the bad guy. Here, he’s the reactionary traditionalist who is also speaking common sense: that a man living alone in the woods with his five children is dangerous and maybe even crazy. When he’s told about Noam Chomsky Day, the best line in the film is Langella’s dryly bewildered response: “I don’t even know who that is.”

Left-wing and right-wing: It’s all about Viggo. With almost any other actor in the role (like, say, Willem Dafoe), Ben would probably have come off as a starry-eyed woodland progressive. But Mortensen, who looks like he’d be perfectly at home playing Jesus Christ or Charles Manson, has a leather-skinned macho severity that makes him way too badass to be stuffed into a conventional liberal box. In “Captain Fantastic,” he truly does seem like a hunter, in the Hemingway/James Fenimore Cooper sense. He looks like the kind of guy who, yes, would worship Noam Chomsky, but he also looks like the kind of guy who would eat him for breakfast. It’s the ruggedly paradoxical, gentle-but-brute presence of Viggo Mortensen, more than anything else, that makes “Captain Fantastic” a twisting Rubik’s Cube of blue and red.