According to the 1987 book American Football:
Every football game is preceded by a playing of the American National anthem. Rivalries are temporarily forgotten as fans and players stand to pay tribute to their country.
Sociology of American Sport (1978) says:
The concern of league officials is exemplified in the efforts of Pete Rozelle, commissioner of the National Football League, to have all players show proper respect for the national anthem (the athletes are told how to stand, how to hold their helmets, etc.)
Additionally, Win Peace and Freedom Thru Nonviolent Action, Volume 7 says of Dave Meggyesy
Meggyesy feels that his first real political commitment came in 1963, his first year in pro football ... The Cardinal management tried to dissuade Meggyesy from his radical involvement, but to no avail. In fact, he went on to make his house a sort of meeting place for the St. Louis radical movement, to circulate petitions among his teammates ... to refuse to stand at attention with the rest of the St. Louis team when the national anthem was played.
For more information, see Meggyesy's 1970 book Out of Their League starting at the bottom of page 245, where he explains that coach Charley Winner (who had been held as a prisoner of war by the Nazis) lectured the team on exactly how to stand at attention during the national anthem. Then he writes:
I'd thought a lot about this and decided that saluting the flag was ridiculous. Every time I even looked at it, I saw only a symbol of repression, so I decided to protest. My original idea was to pull a Tommy Smith by raising my right fist in the air and bowing my head. ... When the National Anthem started I stepped out of line and began kicking the dirt and holding my helmet down in front of me with my two hands. My head was bowed and I was spitting on the ground and moving from side to side scuffing the ground with my shoes.
So not only is standing for the national anthem at profession football games a long tradition, the idea of refusing to stand at attention as a form of protest is as old as the 1960s.
Generally speaking, the tradition that football players (not necessarily professional) should remove their helmets and stand at attention during the National Anthem, facing the flag or facing the music if there is no flag, is at least as old as the 1950s, as explained in the Michigan High School Athletic Bulletin:
Participants in football uniforms should remove their helmets and stand at attention with the helmet held in the hand at the side.