Despite increases in pay, the rules persist in part because supply outweighs demand. Most teams employ only a few dozen cheerleaders, who must audition along with hundreds of other candidates every year to keep their jobs. In the case of the Saints, cheerleaders are limited to a maximum of four years with the club. Yet thousands of women are eager to join the squad.

To be sure, there are cheerleaders for whom the good experiences far outweigh the bad.

“Cheerleading changed my life,” said Flavia Berys, a former cheerleader for the San Diego Chargers who wrote books on audition secrets and became a real estate lawyer. “When I was an N.F.L. cheerleader, I learned a lot about how to speak to the media, I learned about the rules of decorum and professionalism. We were taught how to interact with the staff and the players, and everything. The training we had was all for a reason, and looking back, I think it was all for the right reasons.”

Nearly every N.F.L. team owner is a man, though some cheerleader programs are run by female executives. The league lets the teams establish their own rules for cheerleading squads.

Cheerleaders are seen as an integral part of the game-day experience, well-established entertainment that fans and television networks have come to expect at sports stadiums. For decades, many teams have subscribed to the philosophy that sex sells, so cheerleaders dress in skimpy outfits, wave pompoms and dance suggestively throughout football games, where the majority of fans are men.

But for all their upbeat energy on game days, cheerleaders toil under intense scrutiny, based on the rules included in the handbooks issued by nearly a dozen N.F.L. teams, as well as many of the unwritten rules of the job.

For several years, the cheerleaders for the Saints, the Saintsations, had to sell glossy calendars of themselves in bikinis. Before each home game, cheerleaders walked outside the stadium and tried to sell their allotment of 20 calendars to fans, many of whom had been drinking. If they failed to sell all 20, the cheerleaders had to wander the stands between quarters.

“You walk by a guy and you’re afraid you’re going to get touched,” said Ms. Davis, the former member of the Saintsations fired in January for the Instagram post. “Every girl dreads going out there before the games. We didn’t feel very important because we were literally thrown into the mix with the fans. Who would throw professional cheerleaders, walking around with cash, out with drunk fans?”