“Saturday Night Live” is a tremendously popular show with a tremendously difficult problem to overcome on a weekly basis: being equally entertaining and relevant to a liberal Brooklynite and a conservative rural Alabamian. That’s become a particularly difficult challenge in these divided times.

As the holidays roll around (and happen to coincide with the potential impeachment of President Trump), rather than focus directly on the goings-on in Washington, the show’s cold open on Saturday tackled the rest of us by showcasing three families enjoying holiday meals in San Francisco; Charleston, S.C., and Atlanta. The takeaway: We have more in common than we think. It’s a common refrain for the show. Three years ago, in one of its more well-known modern sketches, Tom Hanks appeared as a white, MAGA hat-wearing Trump voter on “Black Jeopardy!,” only to learn he was no different from the other contestants.

On Saturday, the three households — a stereotypical ultraliberal San Francisco family who prays to “gender-neutral spirits,” a black Atlanta family more concerned with whether Martin Lawrence has still got it than with politics, and a conservative Charleston family with one frustrated liberal member — talk around and about impeachment.

“Those three families may seem different, but, see, they have one important thing in common. They live in states where their votes don’t matter,” Aidy Bryant’s snowman narrator, who hacked into three Nest cameras to gather these stories, tells us at the end of the sketch. “None of them live in the three states that will decide our election. They’ll debate the issues all year long, but then it all comes down to 1,000 people in Wisconsin who won’t even think about the election until the morning of. And that’s the magic of the electoral college.”

In San Francisco, Bowen Yang’s character says Trump “violated the constitution, and there must be consequences.” Over in Charleston, Beck Bennett sits at the head of the table and says: “Well, they did it. They’re impeaching Trump. It’s a disgrace. What crime did he even commit?” When Mikey Day as the young liberal son complains, Heidi Gardner’s character retorts that Trump committed “the crime of being an alpha male who actually gets things done.”

Meanwhile in Atlanta, Kenan Thompson wonders if “Bad Boys III” is going to be good or not. “I mean, it’s got to be good,” he says. “Will Smith and Martin Lawrence back together!” When the younger Chris Redd surprises himself by asking if they could discuss politics instead, Thompson says: “Oh, you mean how Trump is definitely getting impeached and then definitely getting reelected? I’m good.”

The brief sketch draws constant parallels between the three families, sometimes comparing and sometimes contrasting. The folks in San Francisco can’t believe anyone would vote for Trump after this. The family in Charleston can’t believe anyone wouldn’t vote for Trump after this. Thompson wonders who is getting voted off next in “The Masked Singer.”

Buchanan County is one of 31 counties in Iowa that voted for Obama in 2012 and Trump in 2016. Could it swing back to the Democrats in 2020? (Ray Whitehouse/The Washington Post)

Redd continues pushing politics talk, saying people won’t vote for Trump in this coming election. “What people?” Thompson responds. “White people? If white people tell you, ‘I might not vote for Trump this time,’ you know what that’s called, right? A lie! Nobody was gonna vote for Trump in 2016 either, and guess who did? Everybody!”

It continues like this for a while, the discussion touching on Christmas songs, Democratic candidates and even former president Barack Obama, until the families finally reach the thing they all have in common: discussing the NFL in the midst of prayer.

In San Francisco, the “secular blessing of thanks,” ends with: “Thank you for the Super Bowl halftime show, and that’s it.” In Charleston, Bennett prays to the “original American Jesus,” saying: “Thank you for no more kneeling in the NFL. That was very hard for me.” In Atlanta, the prayer is to “historically correct black Jesus.” It goes: “Thank you, Lord, for the not one, not two, but three black quarterbacks who beat Tom Brady this season. Colin Kaepernick, you move in mysterious ways.

The button, or final punchline, of the sketch comes when Kate McKinnon bursts onto the screen as Greta Thunberg, a teenage climate change activist whom Time named person of the year, to tell us that “in 10 years, this snowman won’t exist … and the elves will drown.”

The sketch may have lacked an elegant shape or a neat, easy tagline. But it was one of the funniest openings SNL produced in years, once again showing that the show best succeeds by tackling politics in a creative way, rather than regurgitating headlines.