Private business & public opinion punishes people for exercising free speech rights all the time.  Has throughout the history of our country.  What are you talking about?  The Barnette decision said a school (government entity) could not expel children for refusing to say the Pledge of Allegiance. That's not the same as a private employer firing (which Kaepernick wasn't, btw) or refusing to hire an employee who has exercised speech rights

The only right Kaepernick has not to be punished is not to be have his speech considered a crime by the government (with "fire in a crowded theater" exceptions).  Punishment by one's employer is nothing unusual.  The guy who videotaped himself chewing out a Chick-Fil-A cashier - gone within a day, and fired from his next job when the boss found out he was the CFA guy.  Last I heard he was on food stamps.  The head of Firefox forced out of his position because he supported traditional marriage.  And for something closer to home, google Ward Churchill.