The N.F.L. declined to comment about Davis’s claims.

The Davis case, though, centers on a fundamental league rule. The league’s personal conduct policy, which applies to all N.F.L. personnel, prohibits “any forms of unlawful discrimination in employment based on an individual’s” race, color, religion, sex, national origin, age, disability or sexual orientation, “regardless of whether it occurs in the workplace or in other N.F.L.-sponsored settings.”

Davis argues that she qualifies as “N.F.L. personnel” and that the regulations that cheerleaders must follow violate that policy because they apply only to women. Legal experts say that she might prevail if the team cannot show why women need to be protected more than men.

“It’s illegal for employers to discriminate against women and other groups protected by law,” said Greg Simpson, an employment lawyer in Minneapolis who handles many E.E.O.C. cases. “But sometimes it’s hard to tell if an employment policy or practice crosses the line if the policy doesn’t single out women or minorities, but in practice has a harsher impact on them. These kinds of policies can still be legal if the employer shows it’s necessary for the operation of their business.”

Davis is arguing that the restrictions go too far and that the Saints’ enforcement of them is overly aggressive.

“They’ve been told that anything beyond ‘hello’ and ‘great game’ is too personal,” said Lora Davis, Bailey Davis’s mother and a longtime choreographer for the squad, known as the Saintsations. “It’s considered fraternization to say anything beyond that.”

Now 22, Davis was told by another cheerleader of rumors that she was seen at a party where a player was also present. Team officials called a meeting to discuss the rumors. She denied being at the party, and the team told her it had no evidence she was there.

She told her supervisors that she was contacted by players on social media, but did not respond to them. The team reminded Davis and the other cheerleaders to block players from following them on social media, and to all change their social media presence from public to private even though the players are not required to block cheerleaders from their accounts.