Private banning of speech doesn’t prevent the individual from stating those claims elsewhere. Government mandated banning of speech does prevent that speech from being used elsewhere.
If I don't want someone to speak at my event and ban them, that's not the end of the world. There are probably others who would allow them to speak.
If the government bans someone from speaking, there is no recourse.
This is the state of the world in the USA and one of our cornerstone negative freedoms.
Private banning of speech doesn’t prevent the individual from stating those claims elsewhere. Government mandated banning of speech does prevent that speech from being used elsewhere.