Around lunchtime on Tuesday, a Rolls-Royce stopped at the intersection of Beverly Drive and Dayton Way in Beverly Hills, California. Local people in athleisure walked past Balenciaga, Dior and Prada boutiques, as visitors on Hollywood bus tours ogled nearby Rodeo Drive, where Burberry and Louis Vuitton shops meet at a celebrated street corner.

Up the street, across from the upmarket Erewhon grocery store – home to $21 smoothies – a few diners sat outside an American landmark: the Cheesecake Factory.

The beloved restaurant chain began here in Beverly Hills in 1978; now it has hundreds of locations across the US and Canada. And this week, it’s become the US’s latest surreal culture-war touchstone.

It started when Barack Obama, campaigning for Democrats in Ohio, made a joke that hit Donald Trump right in the real estate. Referring to his successor’s remodeling obsession, the former president said: “He’s got the White House looking like Saddam Hussein opened a Cheesecake Factory. Just gold everywhere.”

The joke was about maximalism: Saddam had 100 palaces and loved gold plating, and the Cheesecake Factory, while affordable for many, offers swanky surroundings that a curmudgeon might describe as over the top. While the Beverly Hills restaurant has a fairly staid interior, a nearby location at Los Angeles’s Grove mall has a grand staircase, floral paintings on the ceilings and an ornate balcony.

Obama’s comments got a laugh at the rally – which surely contained many Cheesecake Factory customers – and went viral. It’s likely the former president knew he would touch a nerve, given Trump’s twin fixations on remodeling and on Obama himself.

Then the backlash began.

Asked by a reporter whether he had a response to Obama, “who made fun of the Cheesecake Factory, comparing it to the White House”, Trump spent nearly two full minutes explaining that the work had been done by the “finest artisans”, that Obama “doesn’t notice dirt and filth” – a racist trope – and that Trump himself only spends “five minutes a day, 10 minutes a day” addressing the problem. (Later that day, he spent another 10 minutes talking about it.)

But the framing of the question – posed by a reporter for LindellTV, founded by the Trump-supporting My Pillow founder Mike Lindell – pointed to what has become a rightwing talking point: the out-of-touch Obama, these critics claim, was mocking restaurant for regular people. The Cheesecake Factory isn’t cheap – a burger will run you about $20 – but it’s positioned as a treat that won’t break the bank.

The conservative political strategist Corinne Clark Barron tweeted: “KEEP THE CHEESECAKE FACTORY OUT OF YOUR ELITIST MOUTH.” On CNN, the New York Post columnist Lydia Moynihan said the remarks showed “how elitist he and the party that he continues to lead has become”. On Fox News, a chyron announced: “Obama criticized for Cheesecake Factory ‘snobbery’.”

This seems to deliberately misconstrue the joke’s primary target, which was the president, not the restaurant. It also conveniently forgets the first half, about Saddam Hussein, who was not known for minimalist taste. Nevertheless, the pitchforks were out, and the Trump administration deployed a true man of the people – the treasury secretary and hedge fund founder Scott Bessent – to dine there.

In fact, he “always” does, as he was at great pains to point out. “I had a great meal, always have a great meal,” he told a Fox Business reporter. He ordered “what I always have: the French Dip Cheeseburger”. Bessent, whose net worth is roughly $600m, said he would “tell the Martha’s Vineyard set to give it a try”.

The median home price in Beverly Hills, home to the first Cheesecake Factory, is $4m; the restaurant itself is far more affordable than the 90210 zip code might suggest. But as Bessent himself proved, the restaurant’s clientele includes plenty of elites: Jennifer Lawrence, Miley Cyrus and Drake are all reportedly fans. It’s a stretch to suggest Obama was punching down here.

That said, given the fierce devotion the restaurant inspires, Obama was perhaps taking a risk even mentioning it – especially at a time when the cost of living is on the ballot. “I think it’s a little bit sad that the pettiness of politics would create that soundbite, knowing all our challenges going on in the country today,” Rick McCormack, who helped create the restaurant’s decor, told CNN’s David Mack. Odes to the restaurant and its “affordable opulence”, as Mack puts it, abound.

In the Atlantic, Elaine Godfrey praises its “sumptuousness: the orange, inviting glow from the knobbly chandeliers; the floral frescoes and painted columns; the generous fountain pops and the dense wedges of cake”. A Redditor puts it more simply: “I can eat the whole plate of food like a savage and waddle to my car afterward with a piece of cheesecake to go.” The food is indeed good, and plentiful: the chain is known for its enormous and diverse menu, with items ranging from fried mac and cheese to avocado egg rolls to vegan cobb salad. There’s also, of course, lots of cheesecake, including but not limited to the mind-boggling Oreo Dream Extreme. On Tuesday, the chain reported third-quarter revenue of $1.03bn, up from $907.2m a year before. It’s routinely named among Fortune’s 100 best companies to work for.

In short, everyone loves the Cheesecake Factory, from Birmingham, Alabama, to Des Moines, Iowa, to Beverly Hills, where the autumn sun shone this week over warm baskets of complimentary bread. Surely it can take a joke.