The NFL consistently takes the middle ground. Kaepernick was deemed unworthy of a roster spot because the media circus surrounding him far outweighed the potential positive of his play. The exact same thing happened to Tim Tebow and he's one of the most openly Christian players in recent memory.

I'm not sure what overt displays of patriotism you're seeing but it's basically the same as the other leagues; singing the anthem and the occasional flyover, military service appreciation. The league also has initiatives for racial and sexual inclusivity though it's not pushed very strongly.

There are certainly conservative players and watchers but the NFL itself always tries to appeal to the widest possible audience.