I may see the confusion, so I'll try to clarify a distinction that's not always made: Two things that intersect touch very briefly at the intersection and move on—the intersectional model implies different forms of oppression are like separate roads that cross wherever someone encounters two or more prejudices at once, but otherwise, they're unrelated.

The older socialist model is more complex: we see different forms of oppression springing from the same roots and growing together. That's why Malcolm X said you can't have capitalism without racism and King said we need democratic socialism.