The 'etiquette' varies from session to session, IME (I assume we are including what some people call "singarounds" in this).

Some sessions or singarounds are open to everyone to all comers - I would call this an open session or open singaround (or "come all ye" as they used to be called). If a session is not open to outsiders, I suppose it would be a closed session. I'm not aware of any closed sessions myself, but I suppose they must exist - I guess there would be no point in advertising them though. A closed session would be private and so shouldn't concern others. I suppose the 'cliquey' session would be something like that though, where they only grudgingly let others join in.

Most people know their limitiations and will keep quiet if they can't keep up or don't know the tune/chords etc. The problem comes when someone doesn't know but persists in playing regardless. These people must be thick skinned as well as tone deaf and I'm not sure how you could deal with them without being rude.

For singarounds/playarounds, where each person has a turn, I prefer it where the default is for the others to shut up, unless invited to join in by the performer. But I've been to some sessions where people seem to join in as a matter of course, even when they have their own turn. I guess in that case you could "retaliate" by "noodling" or whatever while they are playing/singing - maybe that might get the message across - but I somehow doubt it. Again, these people are probably a bit thick skinned.

I agree that sensitivity is the answer, and most of us have that. It just takes one person to spoil a good session though.