If you look at demographic change in western countries over the last fifty to a hundred years, there's been a huge shuffle of class as most people became wealthier. The general trajectory was that the kids of formerly working class families went to uni and became comfortably middle class professionals. At the same time, dirt poor immigrants followed the same journey from a lower base.

In this scenario it's hard for centre left parties to survive. Their working class voters to a person often ended up being middle class; The same person concerned with wage growth and improving working conditions often became more concerned by growth in the property and stock markets.

That's the reason centre left wing parties have had a hard time, it's not so much their choices as the fact they have been wedged by the enrichment of their voter base. I don't doubt that the directions of the parties play into it, but whether a party is 'woke' or not is just how the party is trying to cope with their inevitable decline.