Intersectionality is a concept, not a theory. It is a description of how different forms of oppression--racism, sexism, LGBTQ oppression and all other forms--interact with each other and become fused into a single experience. ... Intersectionality is another way of describing "simultaneity of oppression," "overlapping oppressions," "interlocking oppressions" or any number of other terms that Black feminists used to describe the intersection of race, class and gender.
Marxism explains all forms of oppression as rooted in class society, while theories stemming from postmodernism reject that idea as "essentialist" and "reductionist." This is why a number of Marxists have been dismissive or hostile to the concept of "intersectionality," without distinguishing between its competing theoretical foundations: Black feminism or postmodernism/post-structuralism.
The concept of intersectionality was first developed by Black feminists, not postmodernists. Black feminism has a long and complex history, based on the recognition that the system of and, since then, modern racism and racial segregation have caused to suffer in ways that are never experienced by white women.
I believe it is a mistake for Marxists to lose sight of the value of the Black feminist tradition--including the concept of intersectionality, both in its contribution to combatting the oppression of women of color, working-class women and the ways in which it can help to advance Marxist theory and practice.