Denmark's "Troll Trace" company built a sentient AI robot to put a stop to America's "hyper-masculine" war addiction, and bring them under rule by a global government in the name of "world peace". He was originally a mannequin from a department store in Montreal that they stole, then programmed the Troll Trace machine learning algorithm in, and brought to life by plugging him into a hundred hair dryers. The Danish government installs him as a Trojan horse in dangerously close proximity to the troll capital of the world, the United States, by poisoning Canada's maple syrup supply with Member Berries to make them nostalgic for the years of Pierre Trudeau.
Trudeau-bot confuses the drugged-up Canadian public with the ultimate paradox: He claims to be a "feminist," who doesn't want people to judge each other by appearances, while at the same time he became PM by making "strong, empowered women" all wet with his shirtless selfies (another propaganda campaign by the Danes).
Canada annexes the United States during a rare period of radio silence from Donald Trump, who has had his Twitter account deleted by Troll Trace, and been abducted and sent to Scotland to play golf under strict orders of the Danish anti-troll army. Hillary has died unexpectedly, so millions of disaffected female Democrats managed to get Jill Stein to overturn the election result and hand over the presidency to the constitutionally ineligible but otherwise perfect Trudeau.
The girls are happy that they "smashed the patriarchy" while ignoring or oblivious to the fact that they did so to get the attention of a guy they're crushing on. Wives leave their husbands, taking their daughters with them, and all flock to the cult of Trudeau, who gives them pointless ceremonial positions in his cabinet just so he can say he met a gender quota and "it's the current year." Yet he is such an empty suit he can't remember if his own wife's name is Sophie or Selfie.
Eventually, other countries fall to Canadian annexation, while no one notices the economy has collapsed except the boys and men, who have been rendered irrelevant second-class citizens under Canadian occupation, and woefully inadequate when compared with the too-good-to-be-true Canadian PM. Besides them, there's Leah Remini, the only woman in the entire country smart enough to resist Trudeau's wiles (because he reminds her of Tom Cruise, hint hint) and recognize a cult when she sees one.
Cartman snaps out of his nu-male trance that he was in while boyfriend with Heidi, because he is mad that Trudeau made everything so damn expensive to pay for universal healthcare that he can't even afford to buy Call of Duty -- which has been banned as "too violent" and replaced with a stupid role-playing game called "Terrence and Philip's Oppression Quest". He apologizes to Butters for being a dick; Butters then invites Cartman, and the rest of the boys, to gather at a massive conference on restoring masculinity at the now-empty football stadium where the Broncos once played (because football died a natural death with the end of "maleness," and because even the men got sick of Colin Kaepernick injecting politics into it all the time).
The conference is hosted by none other than Milo Yiannopoulos, "king of the Trolls" (in full David Bowie getup) and cousin thrice-removed of Big Gay Al. Milo invites Gerald Broflovski on stage to describe his strategy of how to defeat Trudeau: troll the egotistical fuck to the point he gets so frustrated he has a nervous breakdown and rips out his perfect hair, causing the Canadian government to collapse -- and with it, the "matriarchy." Gerald explains that this is like Samson in the Bible, prompting another guy in the troll army to ask, "the exploding Bible? I thought that was the Quran." Gerald gets annoyed and says, "not SAMSUNG Bible! Oh, and whatever you do, don't call Muslims violent or they'll kill you. I know this doesn't make sense, but trust me -- we've been through this before."
The American men then take to their computers to harass the Canadian puppet dictator ad nauseam, hashtagging their vulgar memes of Trudeau as boyfriend to Fidel Castro (a reference to the Saddam-Satan relationship from the early seasons), with the phrase #BringBackOurGirls.
In the follow-up episode, they succeed in overthrowing the Canadian parliament and breaking Trudeau-bot to the point where he is as bald as his father due to frustration. They did so by rigging Internet search algorithms with the phrase "Justin Trudeau is a dick like Anthony Weiner," which ends up mixing Anthony Weiner's dick pics with Trudeau's selfies in search results, and shocking the all-female citizenry into thinking he's a covertly misogynistic jerk who lied about being a feminist just so he could exert power over a hapless banana republic of gullible women. He flees Canada and ends up at a sex-addiction rehab clinic in the newly seceded Mexican colony of California, with Weiner, Bill Clinton, and an emaciated Charlie Sheen.
The men then show up in Canada to take "their" women home, but to their surprise and chagrin, they don't want to go; they want to start an all-female government of their own in Canada without Trudeau. But as is typical of leaderless revolutions, the torch-and-pitchfork "Occupy Canada" mob devolves into infighting -- a literal battle of the sexes, with the flames stoked by the Troll Trace CEO. That is, until Donald Trump, having escaped from his golf-course prison in Scotland, shows up unexpectedly in a limo chauffeured by Bruce (Caitlyn) Jenner, who runs over the Troll Trace CEO en route to the Canadian parliament building and crashes into a fire hydrant that spews out maple syrup. Trump yells at Jenner that "she" is the worst chauffeur ever and proclaims "you're fired."
Trump then announces an executive order that women aren't allowed to drive anymore, before Gerald points out to him that this is too severe of a trolling operation, because that's how it's done in Saudi Arabia. So Trump declares instead that women can only drive golf carts, and proceeds to make 50% of caddies female at all Trump-owned golf courses (which is literally the same as Trudeau did with his cabinet ministers). Meanwhile, the still dazzled Canadian people proclaim baby Ike their new Prime Minister and hail him as a Christ-like boy king, for no other reason than he is "so cute -- he looks just like Pierre Trudeau's son." Thus starting the cycle all over again.