I have had little experience of the open mike set up but do find that since I always sing unaccompanied it can be offputting if someone strikes up with an accompaniment no matter how good. In an open session I take my chances but would feel quite ok about asking them not to join in on certain songs. Unless someone is good at accompanying and not just trying to muscle in on the tune it can be a nightmare and I have on occasions been drowned out by players who often have no idea of the tune or my interpretation of it. To be accompanied by a really good player would be an honour but would have to be at my request otherwise its just rude.