The US government has curtailed free speech from nearly the very beginning - see Alien and Sedition acts of 1798, which were used to silence opposition to John Adams. Subsequent acts, like the Espionage act of 1917 for example, also serve the broader goal of silencing criticism and opposition to the government (Snowden is charged under that one, for instance). And then you have active government intervention like COINTELPRO, which of course continues under different guise today. So there is (and always has been) a chill on free speech, in particular any speech that is seen to potentially impact the stability of the state.
Outside that arena, people do have free speech - as in the government isn't going to restrict you. Your restrictions beyond the government are varied - access to people that want to hear what you have to say, outlets that want to broadcast what you say, private agreements you enter into, your ability to yell louder than someone who would rather shout you down, etc.
Sterling is an example of someone who entered into a private agreement with the NBA. He can still say whatever he wants, but his continued association with the NBA is subject to that agreement (and the will of the NBA to enforce it, which the previous commissioner was not willing to do). Sterling is apparently monumentally stupid, as he allegedly knew that his mistress was taping him...given his history, I suppose he though he'd always be able to buy his way out of trouble with another donation to the NAACP.
Sterling aside, if you want to work for Catholic charities, one of their terms of employment is to be a professing Catholic. If you go on Twitter and talk shit about your employer, they may be able to fire you under the terms of your employment contract and state law. You might settle a lawsuit with a business and agree not to talk shit about them as a term. Being an employee or entering into a private contract puts constraints on you, but these constraints are economic, not government edict. The degree to which those economic constraints on public speech are important to an individual depends on things like personal wealth (who cares if I get fired), autonomy (if you own your business, you won't get fired), and of course community mores (for instance, the impact of the ChikFilA owner's bigotry varying according to community).
Also at play in public cases: the FCC ceased enforcing the fairness doctrine under Reagan and the language was formally struck under Obama. The obligation for holders of broadcast licenses to be fair, equitable, and honest as a term of that license disappeared.