"The idea that one should or should not sing songs in accents other than one's own, or songs from one's own culture would rule out a large percentage of the middle and upper classes, or anyone that uses 'Received Pronuncation'"

These are two separate, if related issues: 1) singing songs in affected accents; 2) singing songs supposed to be from a culture not one's own. One might fully approve of one practice but not the other. Or vice versa.