Actually, they really don't, unless the team or league says so. The First Amendnent protects citizens from criminal punishment for "speech." It absolutely does not restrict the right of a team or a league, which are private entities, from prohibiting a protest of this nature or speech of any kind on private property. For example, there are many homeowners associations which prohibit the placement of political campaign signs in resident's yards...It is astounding to me how many Americans fundamentally misunderstand the First Amendment, and many other of our Constitutional rights. I guess we can chalk that up it up to poor education re government, civics, etc. in our schools.
Well really they do have the right to do it, its just that the league or team also is with in their rights to discipline them. But I do agree that there is a fundamental misunderstanding of what the First Amendment means.