A public performance, open to all, will attract those people who enjoy the type of music on offer. Music associated with black cultures will attract more black people than music associated with white cultures - and vice versa. Modifying the music probably satisfies no one.
Racial bias or prejudice would only be shown if the presence of ethnic groups was made difficult.
There is no problem in 'clubs & sessions where middle class white people go to sing olde Englishe & Scottishe folke songes and play the Irish tune', provided that anyone is welcomed (which has been my experience).