Riham Osman was marched out during her first day of work at Dulles International Airport outside Washington within half an hour of arriving at her new summer job. Her position as a passenger service agent with Air France was the first job she’d had since making the decision to begin wearing the Islamic headscarf, or hijab, which her new employers were now demanding she remove to comply with their dress code.

“Until that moment, I had never felt a conflict between being an American and being a faithful Muslim,” Osman, 23, said about the 2011 incident. “Now here was someone telling me that it was a problem.”

As a devout Muslim, Osman would not agree to remove her hijab, which many Muslim women view as an essential expression of their faith, and decided to challenge her firing from Air France with the help of the U.S. Equal Employment Opportunity Commission. While the airline eventually changed its attire policy after being threatened with a lawsuit by the workplace advocacy agency, the experience nonetheless left an indelible mark on Osman, who now works as a communications coordinator for the Muslim Public Affairs Council.

Osman is among many Muslim women around the country who are closely watching Wednesday’s Supreme Court hearing in the case of an Oklahoma woman who claims to have been illegally denied a job at Abercrombie and Fitch because of her hijab. The case is seen by some as a landmark opportunity to address what they say is widespread discrimination against Muslim women who choose to cover their hair in the workplace.

“With this case, we’re literally being told by our government whether or not we belong,” said Amani Al-Khatahtbeh, a media relations specialist with the American-Arab Anti-Discrimination Committee in Washington. Should the court recognize discrimination in this case, it would “make a tremendous statement that being an American and being Muslim aren’t exclusive from one another,” she said.

Al-Khatahtbeh’s group is one of the many organizations that have filed amicus briefs supporting Samantha Elauf, who was denied the Abercrombie sales job at a store in Tulsa in 2008, when she was 17. The company has argued that its policy forbids employees who interact with customers to wear head coverings and that it was Elauf’s responsibility to inform them at the time of her interview that she would require religious accommodation, according to the Huffington Post. However, Elauf’s lawyers have maintained that she is protected by the Civil Rights Act of 1964, which outlaws employment discrimination on the basis of characteristics like race, sex and religion.

Women who choose to wear the hijab are protected by the legislation along with the First and Fourteenth Amendments of the U.S. Constitution, which bar federal and state governments from making laws that interfere with the free exercise of religion. Despite these legal protections, 69 percent of women who wear a hijab report facing discrimination, as compared without 29 percent of women who do not cover their hair, according to the American Civil Liberties Union. Nearly 60 percent of Muslim American women say they wear the hijab at least some of the time, including 36 percent who say they wear it in public, a 2011 Pew Research Center survey reported.

The underlying problem that has created so many challenges for Muslim women is a general ignorance about Islam across the U.S. and the lack of contact that many Americans have with regular, everyday Muslim Americans, said Noha Mohamed, a doctor and assistant professor in internal medicine and pediatrics at University of Arkansas for Medical Science in Little Rock. “When I first moved to Arkansas, patients used to think I was a Christian nun and ask me to pray for them,” she said.

Mohamed said people she encounters are now increasingly aware that her headscarf is a symbol of her Muslim faith. She said she has never faced any direct discrimination at her job and has instead encountered more innocuous kinds of misconceptions about her faith. “I heard one mom explain to [her child] that Islam was a culture, not a religion,” she said. “They’re never rude about it; they just don’t get it.”

Only 38 percent of Americans have reported knowing someone who is Muslim, according to a 2014 Pew Research Center survey, which also found a link between knowing a member of a group and having a relatively more positive view of that group. Participants who said they did not know any Muslims were more likely to have negative views about them.

For Al-Khatahtbeh, cases of workplace discrimination against veiled women represent a slice of the many problems that have faced Muslim Americans since Sept. 11, 2001, the aftermath of which she said created a rift between Muslim identity and American identity for many. Since 2001, the EEOC has reported a 250 percent increase in religion-based discrimination claims involving Muslim Americans, with more than 20 percent of its 2012 religious discrimination claims filed by Muslims. A 2010 Gallup survey also found that Muslim Americans were more than twice as likely as Jews, Catholics or Protestants to say they had experienced discrimination.

The fear of discrimination is often most particularly pronounced for hijab-wearing women during the hiring process. “If I wanted to apply for a receptionist position, think about the manager who’s doing the hiring,” said Al-Khatahtbeh. “They’re going to know the first person that their clients see is a veiled Muslim woman, and obviously their decision is going to be linked with their own personal biases and stereotypes that they and the public attribute to Muslim women.” These fears are backed up by a 2013 study conducted by the University of Hawaii-Manoa, which found that all aspects of the hiring process, from callbacks to interaction time with potential employers, were hurt by wearing a hijab.

Prevailing stereotypes about Muslim women, in particular around their supposed submissiveness and subservience to men, can make breaking into the job market an uphill battle for many hijab-wearing women, said Osman. “I know plenty of Muslim women who fear that people won’t take them as seriously because of the image of Muslim women in the media,” she said. “It’s always in the back of your mind, ‘am I going to miss out on opportunity by choosing to wear the hijab?’”

Some of the underlying prejudices that potential employers may have about Muslim women are usually in evidence during recruiting season, according to Safa Elshanshory, a management consultant in Houston, who said her hijab has in the past led recruiters to make assumptions about her political views and religious practice. “I’ve had recruiters pull back their hands from handshakes and ask ‘oh, are you allowed to do that?’” she said. “And, of course, the recruiters … who want to get my take on the Israeli-Palestinian conflict.”

Even after getting a job, the fear of being seen as too demanding can often prevent hijab-wearing Muslim women from requesting accommodations for their religious practice, said Asma Peracha, a first-year law student at NYU Law School in New York. “If something is a constitutional right, we shouldn’t feel ashamed to demand it,” said Peracha, who acknowledged that although she’s been lucky enough to work and study in progressive, accepting environments, she nonetheless sometimes worries about inconveniencing others with requests to accommodate her religious practice, including taking a few minutes for prayer. Peracha hopes that if the Supreme Court rules in favor of Elauf it will set a positive precedent and foster the kind of environment that would help Muslim women feel more comfortable asking for certain kinds of religious accommodations.

Being in a position where she often has to deal with what she called “the old boy’s club” of the energy and oil industry, the Houston-based Elshanshory said she has actually relished using her job as an opportunity to dispel stereotypes about people of her faith. “My presence in the hallways of BP or Conoco or whatever client is almost never expected,” she said. “Most people are like ‘hmm, what is she doing here?’ Once they find out I’m a management consultant, then it’s like, ‘I wonder if she can speak English?’ You kind of see the onion being peeled back layer by layer. Literally just being normal, personable and agreeable and you can walk out of a one-hour meeting have changed a person’s perception.”

This is why Elauf’s case is so symbolically important for many Muslims around the country, according to the Al-Khatahtbeh of the ADC. “Right now we’re in a moment where the tide is turning and we’re seeing a very massive shift in the way that we address Muslim American issues,” she said. “We’re seeing Muslim women breaking down barriers and asserting their place in the public realm and American society to take back the narrative around their own identities.”