The true marxist based left is not woke. It never was. There’s a reason that the western left turned liberal in the 50s and 60s and focused on reform. The CCP killed any thought that decentralized communes could be self-sufficient and centralization killed any concept of liberalism and a responsive command economy. If the majority can vote their way into resources, minorities suffer. With no opposition checking the ruling party, corruption sets in.
If you are referring to the American Democratic party, they are liberal and not left.