At the Newseum gift shop, the top-selling items don't pertain to freedom of speech or the press. Instead, what sells is anything associated with the man who has dubbed the media "the enemy of the people."

President Donald J. Trump.

It's a similar situation at the National Archives, where employees struggle to keep the shelves stocked with Trump shot glasses.

"We sold out of them," said Angela Catigano, the director of retail and e-commerce. "The 8th grade boys seem to love those."

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Trump's election presents Washington's many museums and monuments with an attractive business opportunity.

As the weather warms and the tourism season ramps up, thousands of Trump supporters have begun to descend on the capital, their "Make America Great Again" hats blooming like poppies across the Mall.

Any new president triggers a surge in demand for souvenirs. "Obama memorabilia is selling like hotcakes," declared a Washington Post headline in 2008. But not all museum shops are pushing Trump paraphernalia. Some ignore the 45th president altogether. Others carry only a few items.

What to sell has always been a tricky question for museums and monuments, where tacky items can undercut serious exhibitions. With a president as polarizing and unpopular in the polls as Trump, it's a conundrum that occasionally pits profit against principles.

At the national museums, which don't charge admission and rely on federal funding, souvenirs and memorabilia can be an important source of revenue.

In January, the National Museum of American History pulled a book on Trump from the shelves of its gift shop after The Washington Post revealed that the US$50 (NZ$71) "collector's vault" item was riddled with falsehoods.

Linda St. Thomas, a Smithsonian Institution spokeswoman, acknowledged the error, but said all Trump material had been taken down shortly after the inauguration.

"We did the same for Obama," she said, adding that Smithsonian gift shops "try to stay close to the mission of that museum."

Some museum shops avoid problems by steering clear of politics altogether. A reporter saw no mention of Trump or Obama at the United States Holocaust Memorial Museum's store. The same was true at the National Museum of the American Indian.

At the National Air and Space Museum shop, Trump and Obama were also absent except for two stacks of postcards, easily overlooked among the aisles of astronaut ice cream and stuffed animals in space suits.

At the Washington Monument's tiny gift outpost, Obama was prominently featured on the covers of a biography for children, a presidential sticker book and a compilation of speeches by famous African Americans. But the only sign of Trump was a tiny photo next to his predecessor at the end of a presidential placemat.

At Mount Vernon, there was similarly little sign of Trump - but for a very different reason.

"We had hats, t-shirts, shot glasses, beanies," a saleswoman said in late March. "But we sold out of just about everything."

At the National Archives shop, Trump paraphernalia was prominently displayed near the entrance to the store. Beneath a framed reproduction of the Emancipation Proclamation stood bobbleheads of the newly inaugurated president, with their arms crossed and blond pompadours wobbling.

Catigano admitted that some visitors were put off by the display, but said the shop had been "cautious" not to sell anything controversial.

"We're apolitical," added Patrick Madden, executive director of the National Archives Foundation. "This is our country's history. Agree or disagree, it's all here."

Catigano said she sought out items that visitors couldn't get from street vendors or at other gift shops. Sometimes she commissions original wares, like the Trump socks she said are currently in production.

When she learned that Trump had restored a bust of Winston Churchill to the Oval Office, Catigano contemplated selling copies of the sculpture until she learned she couldn't because of copyright. She is now scouring photos from inside the White House for ideas of other Trump items to sell.

"We're still in the research phase," Madden said.

Another museum that hasn't hesitated to sell Trump paraphernalia is the Newseum - a private museum on Pennsylvania Avenue run by a nonprofit corporation - where a swathe of its shop is devoted to The Donald.

In the early days of the presidential campaign, Trump's controversial statements earned him an outsized share of media coverage. But he also frequently blasted the mainstream media. Since his election, he has denounced critical coverage as "fake news."

Inside the Newseum shop, the only visible allusion to his administration's frequent attacks on the press was a t-shirt with a definition of an "alternative fact" - the term coined by presidential counselor Kellyanne Conway.

Nearby, a corner of the store was entirely devoted to Trump. A coloring book featured the president in a Superman-like outfit. Dozens of stress-relief toys - each one in the shape of Trump's head - lay piled on top of one another in a basket. There were plush Trump dolls and Trump t-shirts. Trump bobbleheads and Trump books.

There were even chocolate bars bearing the president's smiling face: one for US$2.99 or two for US$5.

"It's the number one stuff in the store," shop employee Were Barnabas said of the Trump gear.

The top seller, he said, was a US$16.99 red hat featuring two rows of stars and Trump's trademarked phrase "Make America Great Again." The store had sold 40 of the knockoff caps that day alone.

"Right now I only have 33 left," Barnabas said, checking his inventory. "That's a really low number. I don't think that will last tomorrow."

One museum shop that would not be selling Trump merchandise was the National Museum of African American History & Culture, said Linda St. Thomas, the Smithsonian spokewoman.

Even here, however, visitors could not escape the president entirely. Outside the museum, next to a hot dog stand, Trump t-shirts hang off a cart like flags from a pirate ship.

The cart moves around the mall, explained Mychau Duong as she readjusted Trump hats riffled by customers.

This wasn't prime Trump merchandise territory, she admitted, "but here we sell some too."