According to a report authored by Senators John McCain and Jeff Flake of Arizona (both Republicans) the military paid out $53 million to sports teams to stage those patriotic displays you often see. This was covered in a local news story in the Pittsburgh Post-Gazette on November 6, 2015.
The patriotic displays are designed with two functions in mind, to promote patriotism in general and to recruit for the military. While it is incorrect to say that players are paid to stand and show respect for the national anthem and the flag, according to the game operations manual:
“The National Anthem must be played prior to every NFL game, and all players must be on the sideline for the National Anthem. During the National Anthem, players on the field and bench area should stand at attention, face the flag, hold helmets in their left hand, and refrain from talking. The home team should ensure that the American flag is in good condition. It should be pointed out to players and coaches that we continue to be judged by the public in this area of respect for the flag and our country. Failure to be on the field by the start of the National Anthem may result in discipline, such as fines, suspensions, and/or the forfeiture of draft choice(s) for violations of the above, including first offenses.”
The displays, which are often lavish affairs, including military flyovers, are often paid-for activities, though we have no way of knowing which events are paid for or how much is paid for each event. Moreover, the $53 million price tag discovered in 2015, and reported before the year ended, likely included other costs to perform these events: such as pay for service members or fuel for aircraft doing flyovers, or other production costs.
Collectively speaking, sports teams received over $53 million in 2015, however in 2016 the NFL actually returned fees it received for the ceremonies themselves, to the tune of $724,000. So, while direct fees were returned for the displays, other forms of paid advertising, on-site recruiting, use of space, and signage were not returned.
So, while there is a cost for these events, the NFL no longer gets paid to allow the event to take place. The production costs are born by the sponsor, but the time is freely given. The game operations manual prescribes a player protocol for the playing of the national anthem, a standard no longer enforced within the NFL.
The military continue, as far as we know, to pay the production costs for these events, despite the fact the NFL players themselves are no longer compelled to show respect for the event.