I think I'd want to respect the individual performer's feelings on that, whichever they want to be part of their performance. It is their presentation of their work, after all, and I think what they say goes. I pay a fee to see the performance as a creation of the performer, therefore I think the performer should have maximum control of it. I accept that when I go to a performance, and if I didn't like that, I wouldn't go, I'd go to a performer that liked people to join in. And there are plenty of other places/opportunities to join in singing if you want to.

And I think that all applies even to an open mike performance.