The law gives very few liberties. And the places where people think it give liberties, it is actually just banning laws from being made around liberties.
Freedom of speech is the peak of this. People think it means "I can say whatever I like wherever I like". But that's not what it is. The government cannot make laws curtailing speech (though, it does... enforcement and interpretation don't line up with the original intent). You can, however, sign an NDA which curtails your speech. A business can kick you out for saying something they don't like. An employer can fire you for saying "poodle" one too many times.
And that's what we are dealing with around airlines. They absolutely can kick you off the plane and ban you for almost any reason. For what you say, wear, or because they don't like how tall or short you are.
The law really only protects a few things. Your race, your gender, your religion. Everything else is fair game for a private institution to discriminate against. They can kick you off a plane because you are a journalist. They can kick you off because you won't quarter soldiers. They can kick you off because you don't submit to a search of all your property.