A round 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.…