The N.F.L. season has not even officially begun, but after just a handful of exhibition games tensions are rising over players’ protests during the national anthem and the league’s handling of the issue.

After a few Miami Dolphins players demonstrated during the playing of the anthem at an exhibition game on Thursday, a county police organization announced it would no longer participate in a discounted ticket program offered by the team. At the same time, Tre Boston, a safety for the Arizona Cardinals, suggested in an interview with The Ringer that N.F.L. team owners had colluded against safeties, implying that they were doing so to justify not signing Eric Reid, who protested alongside Colin Kaepernick when both played for the San Francisco 49ers.

The two statements illustrated how relations between some fans and the N.F.L., and between the league and certain players, remain raw. And with the issue showing no signs of fading, the contentious atmosphere makes it even less likely that owners will be able to find a solution that satisfied all sides.

The statement by the Broward County Police Benevolent Association came after Kenny Stills and Albert Wilson of the Dolphins took a knee during the anthem on Thursday. The association said it had received discounts from the Dolphins to attend the game, at which first responders were honored. The group said it “entered into this partnership with the understanding that the Dolphins organization would require their players to stand for the national anthem.”

But after the demonstrations, which also included Robert Quinn raising his fist, the police group said it would not take part in the discount ticket program and encouraged police benevolent associations in neighboring Dade and Palm Beach counties to follow suit.

It is unclear, however, when the police group reached that understanding with the team. The league changed its policy in May to require all players to either stand for the anthem on the field or stay in the locker room while the song is played.

But the N.F.L. suspended that policy in late July while it negotiated with the N.F.L. Players Association on potential revisions.

The Dolphins declined to comment.

Boston, one of the best free-agent safeties on the market this off-season, suggested in an interview with The Ringer that the owners had conspired to suppress salaries for free-agent safeties. That is the same contention made by Reid, who has filed a grievance against the N.F.L. and remains without a team, like Kaepernick.

Last month, Boston signed a one-year contract worth $1.5 million with the Arizona Cardinals.

“How did we get to a point where this is what we were worth?” Boston asked. “You can put my stats up against some of the best of them you’re going to get me in the $7 million-plus range.”

Boston has been outspoken in the past about police shootings — one of the focuses of the anthem protests. Two years ago he urged a unified response from his Carolina Panthers teammates after a police shooting in Charlotte, N.C.

He is not the only safety who settled for an underwhelming contract this off-season. Kenny Vaccaro, another highly regarded free agent, signed a one-year deal with the Tennessee Titans for $1.475 million.

Reid remains unsigned. During the off-season, he was invited to Cincinnati to speak with the Bengals, where the team’s owner, Mike Brown, reportedly asked Reid whether he would continue to protest during the national anthem.