If you're an NFL fan you can skip ahead a bit. If not, grab a drink and gird yourself: I have to explain a football thing. Without it, the institutionalized racism and "It's OK to be opinionated so long as your opinion is virulently jingoistic and fetishizes the military!" culture won't make sense.
Briefly, at any given moment there are maybe 12 human beings on the planet capable of playing Quarterback in the NFL well enough for a team to reach and win the Super Bowl. For reasons you are not interested in, it's the hardest athletic role to fill in team sports. This explains, if you were curious, why the same few famous names end up in the Super Bowl year after year: Tom Brady, Peyton Manning, Russell Wilson, Aaron Rodgers. Because their teams are lucky enough to have one of the small number of humans who is good enough to get them to the championship. There are probably 10-15 more "OK" quarterbacks who can lead their teams to the playoffs, but only a few truly elite ones.
I mention this to preface the point that anyone – ANY ONE – with the merest glimmer of talent at the QB position is given dozens of opportunities to play until he has failed so many times that there is absolutely, conclusively no doubt that he doesn't Have It. The shortage of QB talent is so acute that even a hint that a guy can play is worth a look. Played well in college? Bring him in! Had a couple good games as someone's backup? Bring him in! Led the Biloxi Deer Ticks to the Mississippi Semi-Pro Football Conference title last year? Bring him in!
A football fan friend and have a running joke about a forgettable player named Jason Campbell. Because he started for a team once (and was not good), he attracted the label "Former starter" or "capable of starting" and parlayed it into a long career with many teams. He was never good, yet team after team would bring "former starter Jason Campbell" in and give him his 37th chance to prove himself a good QB. He wasn't.
OK. Now. In context, Colin Kaepernick took a team to the Super Bowl. Not "showed potential to." Not "Played in the Super Bowl of the Norwegian Summer League." The actual Super Bowl. And. AND. His team came within one iffy referee's call of winning that game. His game has shortcomings and he has played less spectacularly since that Super Bowl – again, not worth going into – but he took a team to within one play of a championship in a league that will give literally any bum whose arm hasn't fallen off multiple shots. Now, he can't find a job and more than a few of the bolder voices in the sport are starting to wonder.
Is his style on the field unconventional? Yes. But you cannot and will not convince me that in a league where winning is everything, coaches get fired if they don't produce, and teams spend billions shooting for Super Bowls that no team would look at his body of work and think "Let's have him in for a look-see. You remember him, he's that fella who almost won the Super Bowl that one time."
You will not convince me – football reference joke ahead – that a league in which Josh McCown is on his TENTH team and is being handed a starting job yet again despite never having done so much as sniff a winning record has no use for Colin Kaepernick on the field. Teams routinely sign guys proven beyond any shred of a doubt to be mediocre or worse with no room for improvement. No league in which a coach can convince himself that he's going to ride Mike Fucking Glennon to a championship is one in which a coach cannot look at Kaepernick and think, "I'll recapture the magic!"
So when players grumble that Kaepernick has been blackballed for his outspokenness, what they are really saying is, "We have a guy playing QB who can't hit his ass with both hands in his back pockets, and you're telling me Colin can't find a job?" They know. They know better than anyone how rare a QB is, how terrible some of the QBs in the league are, and how many times a player with the tiniest shred of talent is given second, third, eighth, tenth chances to start. But when a guy kneels for the National Anthem or says "Hey it might be nice if cops stopped shooting black people," suddenly his phone won't ring.
It's not hard to figure out. All the excuses in the world can be made and have been made. The NFL has no policy against players voicing their opinions when those opinions are similar to the content of a Fox News comment section. That's just fine. Anything spicier than that, though, and the league can't handle it.
There's no conspiracy. It's a case of the biases being ingrained in the system so thoroughly that nobody even needs to tell teams not to sign him. They wouldn't dream of it.