They would need to find a way to rein in the "woke" leftists which is more savvy than pretending that cultural issues don't exist.

One approach would be to embrace the cultural leftist's concern about culture and make a case that a class-heavy approach is the best way to fix culture too. I think this is a losing proposition because I don't think it's true, and I don't think it can be sold as true.

An alternative approach would be to embrace the counter-woke rejection of many aspects of cultural transformation that the woke movement seeks, making the case that a class-first approach is the best way to remove the pressure on culture and retain as much of existing culture as possible. I think this is also a losing proposition because class-first transformation is too extreme for the cultural conservatives since most of them are also economic conservatives.

So I think the class-first leftists are simply stuck. People taking that approach will probably need to put their long-term ideals on the back burner and take pragmatic approaches for the time being, and re-evaluate later whether a robust class-first approach can work.