What makes this a potential violation of the Constitution is the involvement of the police. If this were purely a private decision by a private club owner, there would not be a Constitutional issue. But if the police were applying pressure on the club owner to silence this singer, then the police have violated the First Amendment and should be held accountable.
As for the club owner, he is within his rights to pull the plug. ...And his customers are within their rights to decide they don't want to do business with someone who censors performers. A boycott would be an appropriate response by any customers who feel that way.
Yes, discovery, there is a Constitutional freedom of speech issue here if the police are applying explicit or implicit pressure to the club owner to silence this performer.
And since you seem a devotee of property rights, I suggest that consumers exercise their own property rights and refuse to patronize this club as long as it censors performers.