Lessons of the inner city
Parents who send their children to private schools have an equal right to membership of the Labour party, and vice versa. It is not hypocrisy. There is no "dissonance" other than that promoted by Ted Wragg which is based on an ideological model of the Labour party no longer valid.
Focusing on historical class-based divisions and failing to recognise the greater significance of new socio-economic demographics - particularly classifications based on crime, drug use, transport infrastructure and property values - is struggling with the wrong enemy.