"Not at all absurd, Shimrod. Any common interest group who choose to come together for the satisfaction of that interest have, quite correctly, the right to include, or exclude, whomever they wish."

Oh dear, have I been caught on the wrong side of the fence!

Actually, I think it's absurd, Don because although singing accompanied is rare in the British tradition it's not unknown and it certainly exists in other traditions (including various American ones). I also think that skilful and appropriate accompaniment can add an extra and exciting dimension to a performance and to deliberately exclude it would mean missing out.
Although I definitely think that any worthwhile club should have some sort of policy I think that this policy should be designed in a way which encourages people to develop their performance skills within a defined framework but does not stifle innovation and is not primarily designed to exclude people. This is probably more or less impossible to achieve - but you must admit that it's a worthwhile aspiration (?).