DETROIT/SAN DIEGO (Reuters) - Businesses shut their doors, students skipped class and thousands of demonstrators took to the streets in cities across the United States on Thursday to protest President Donald Trump’s immigration policies.

Activists called “A Day Without Immigrants” to highlight the importance of the foreign-born, who account for 13 percent of the U.S. population, or more than 40 million naturalized American citizens.

Trump campaigned against the estimated 12 million illegal immigrants, playing on fears of violent crime while promising to build a wall on the U.S.-Mexican border and stop potential terrorists from entering the country.

While the number of participants in Thursday’s protests could not be determined, many sympathetic business owners closed shop and working-class immigrants forwent pay for the day.

“I told my English teacher that I wasn’t going to school, and she said she understood,” said Rosa Castro, a 13-year-old U.S. citizen in Detroit, who marched with her 26-year-old sister, one of several undocumented family members whose future she is concerned about.

Since taking office last month, the Republican president has signed an executive order temporarily banning entry to the United States by travelers from seven Muslim-majority countries and all refugees. That order was put on hold by federal courts.

Immigrant rights groups have also expressed alarm after federal raids last week rounded up more than 680 people suspected of being in the country illegally.

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In San Diego’s Logan Heights neighborhood, a 44-year-old undocumented business owner who identified herself only as Lucia for fear of deportation told Reuters she closed her nutrition shop for the day, costing her $200.

“Our community is frightened and cannot speak out,” she said. “Things are very bad for us with the new president.”

Advocates have called attention to cases such as one in El Paso, Texas, where federal agents arrested a transgender woman as she left a courthouse where she was seeking a protective order for domestic violence.

Virginia Governor Terry McAuliffe wrote Homeland Security Secretary John Kelly to express concern over immigration enforcement in his state, citing an NBC Washington report that agents arrested people outside a church that operates as a shelter from the cold.

Sympathy marches and rallies were held in cities including Raleigh, North Carolina, and Austin, Texas. Thousands joined demonstrations in Chicago and Detroit.

In the Los Angeles Fashion District - comprising some 4,000 apparel outlets, showrooms and manufacturers covering about 100 blocks of downtown - about half the shops in the area’s retail core were closed, along with about 40 percent of one of the large flower markets in the area, said district spokeswoman Ariana Gomez.

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A Southern California grocery chain, Northgate Gonzalez Markets, said it gave employees at 41 stores and the corporate headquarters permission to use paid personal time off to participate.

In Washington, more than 50 restaurants were closed, including high-end eateries.

“As far as I’m aware, all of our immigrant employees chose to take the day off,” said Ruth Gresser, 57, who owns four pizza restaurants in the District of Columbia area. “We have three relative novices and an old lady making pizza,” she said, referring to herself.

At the Pentagon, about half a dozen food outlets were forced to close after staff members joined the protest, a Defense Department spokesman said.

The National Restaurant Association criticized the walkouts, saying in a statement that the organizers “disrupt the workplaces of hard-working Americans who are trying to provide for their families.”

In Austin, hundreds chanting “Say it loud, say it clear, immigrants are welcome here” marched from City Hall to the State Capitol, where lawmakers in the Republican-controlled body are considering a measure to punish sanctuary cities that shield immigrants from federal agents.