Joseann
I don't think the Labour Party is necessarily woke, but it is peripheral in this area and spends too much time on it. There are other inessential issues they major on about too in my opinion. I hope they get down to proper business and leave out all the rest.
They can be oversensitive. But then so can those whose lives have been enriched by conditions of entitlement, should anyone ever suggest those conditions be removed.
I don't think being or not being "woke" is a Labour leadership is issue. I do think being unable to escape the many-faced deprivations of being 'disentitled' is. I think it is Starmer's definition of "working class". He talked about it in his conference speech, refering to his sister. It is something he knows about, having been the only one of four siblings who had found away through a disincentivised world.
Whatever creates disincentives, it does seem a good thing to try and put it right.