(CNN) For some Muslim women in France, it's all but impossible to swim in a public pool and stay true to their beliefs.

Many stay covered as part of their faith with garments such as hijabs, which cover the head, and burqas, which cover the entire body. So they can't just throw on a bikini or even a one-piece when they go to a pool.

Some women wear " burkinis ," bathing suits that keep them covered while they swim, leaving their hands, feet and faces bare. But many cities across France have banned them.

To protest the bans, Muslim women from Alliance Citoyenne, a group in Grenoble that advocates for social issues, began going to swimming pools in the suits last month as an act of civil disobedience.

Swimming as civil disobedience

Alliance Citoyenne said that its campaign is inspired by the actions of black Americans during the civil rights movement, specifically the use of civil disobedience like the Montgomery bus boycott.

Seven women went to a pool in Grenoble once last month and once this week. The group plans similar protests every Sunday until the rule is changed, Alliance Citoyenne head organizer Adrien Roux said.

"Civil disobedience of Grenoble Muslim women for public pools that respect freedom of conscience," the group said in a tweet.

Matthieu Chamussy, a member of the center-right Republican Party, criticized the action on Twitter and asked the mayor of Grenoble what he was doing about it. "New intrusion in swimsuit covering in Grenoble," he said in a tweet. "The city ruling is no longer applied, political Islam is advancing step by step, the cause of women reversing."

Nouvelle intrusion en maillot couvrant à #Grenoble. Action coup de poing menée ce jour à la piscine Jean Bron. Le règlement municipal n'est plus appliqué, l'islamisme politique avance pas à pas, la cause des femmes recule. @EricPiolle que faites-vous? pic.twitter.com/CsOuxS05QC — Matthieu Chamussy (@m_chamussy) June 23, 2019

Grenoble Mayor Eric Piolle later tweeted, "When it comes to equal access of a public service, the role of the state is to pose clear and just rules for everyone. National solidarity is at stake. Refer to the 'individual dialogue' the resolution of tensions in territories is ambiguous and fuels fractures."

Lorsqu'il en va de l'égalité d'accès à un service public, le rôle de l'État est de poser des règles claires et justes, pour tous. Il en va de la cohésion nationale. Renvoyer au "dialogue individuel" la résolution de tensions dans les territoires est ambigu et attise les fractures pic.twitter.com/0h5NhgtuKJ — Éric Piolle (@EricPiolle) June 25, 2019

It's not just about pools

Muslim women in France often have difficulty accessing public services because of their hijabs and can't even accompany their children into schools, Roux said.

This year, the French Senate voted to ban religious symbols on school trips, essentially forbidding mothers who wear headscarves from attending. And now that it's summer, children want to go to the pool -- but they can't unless a parent is with them, Roux said. If their mothers are Muslim and wear hijabs, they can't go.

"So they have to deny their religious beliefs and go, or not deny and not go," he said.

Roux compared keeping covered at a swimming pool to Rosa Parks being able to ride at the front of the Montgomery bus. And he said it's not just about pools.

"The big question is access to public employment, to certain jobs they are denied" because of religious symbols, he said. "Many cannot be teachers in France and other jobs. This is why it's important for them."

A study in January from researchers at Stanford University found that France's 2004 ban on hijabs, Jewish skullcaps and large Christian crosses in public schools had a negative impact on Muslim girls.

Specifically, it reduced their chances of completing high school and affected their ability to succeed in the labor market long term. Further, the researchers argued that the ban reduced assimilation by "casting religion and national identities as incompatible."

Veiled women are often turned away from places that aren't covered under the ban, Roux said. Members of Alliance Citoyenne who were veiled once tried to go bowling but were told they couldn't enter.

"It's illegal, but it still happens," he said.

Fines and threats

Roux said that other pool-goers have generally received the women positively and that some people in Grenoble applauded when they arrived in burkinis.

But when the women got out of the pool, there were two police buses waiting for them, Roux said. The women were fined for their actions this month.

The next day, Roux said, the group received racist comments on Facebook, with people saying they don't want Muslim women in France.

Two women who spoke to the media even received threats in their mailboxes, Roux said.

"Why this is making a big mess, why these national leaders feel the need to comment about these seven women that went to swim, it's crazy," Roux said.

Why is the burkini banned?

France rigorously enforces secularism. Religious symbols aren't allowed in any publicly owned spaces, like public schools. Even lawmakers aren't allowed to wear religious symbols.

Secularism, "laïcité" in French, is deeply ingrained in French culture.

Its roots lie in the French Revolution, when the people rose up against the both the monarchy and the rich, including the Catholic clergy. The separation of church and state was made into law in 1905 -- almost 100 years after the Revolution.

It's also about allegiance. Many believe that French identity is a person's primary identity and that nothing comes before it.

During the 2018 World Cup, comedian and TV host Trevor Noah came under fire from the French ambassador to the United States after suggesting that France's team, most of whom had African heritage, were African and not just French.

When Muslim women move to France, then, many believe that they are now French and must adopt French customs. And that means leaving the hijab or other coverings at home.

A history of the bans

In 2011, France banned burqas and niqabs, which cover the face, in public spaces. Legislators who supported the law, including then-President Nicolas Sarkozy, said the garments threatened French secularism and were debasing to women.