I'm going to have to strike a dissenting note - I don't see what the problem is. Of course it all depends on the nature of the performance. At a formal performance to which entry is by permission (regardless of size or whether or not a ticket is paid for) then both the performers and the organisers are entitled to set house rules which the audience should abide by (although in larger venues these can be difficult to police).

However in a pub session or singaround the situation is very different. In my view, if you are doing something in a public place then other people are equally entitled to record, video or photograph you. The law, in the UK at least, supports that. Now you are perfectly entitled to ask them not to, but not to demand it as of right. If you are uncomfortable with it, then it should be a matter for discussion and negotiation. Good manners comes into it, but frankly it would no more occur to me to ask permission of everyone in a session to record or photograph them than it would occur to me to ask permission of everyone in the pub to play music.

How the recordings are used is another matter, and if they are published then questions of copyright arise and the performer does have legal rights.