Initially, capitalism worked towards abolishing the family with industrialization. But since imperialism, capitalism is stagnating heavily and capitalism no longer works towards abolishing the family (at least in the imperial core).
It seems to me that the working class must work towards industrializing domestic labor and abolishing the family. But I am not sure how that might concretely be organized. It's not really as self-contained as a struggle for national liberation.
Pic unrelated.