Capitalism does not "need" racism

It also does not "need" the steam engine

If your conception of capitalism abstracts from its actual historical existence it's useless

The context doesn't always appear to be clear to people, so here it is:

an influential line of argument says that capitalism is an ideal-typical system of class relations which doesn't "need' racism to function

According to this argument, there is also no inherent necessity for contingent technological developments like the steam engine, since agrarian capitalism predates it

The reality is that capitalism developed as a concrete system and persisted over time by adapting to contingent historical phenomena, often not explicitly "economic" (consider the world interstate system, for example)

Specific technological innovations were not preordained by capitalism's abstract logic, yet facilitated the growth and accumulation required for its expanded reproduction

For an example of this discussion you can refer to the exchange between Ellen Wood and Adolph Reed where the latter quite coherently points out that asking whether capitalism "needs" racism is a nonsense question.

Do your homework

If you think capitalism needs steam engines (they're "material," after all!) and doesn't need racism, you have just engaged in a hilarious failure to understand capitalism

Capitalism's social relations compel the introduction of labor-saving innovations, the adoption of any particular innovation is contingent

Capitalism also requires the proletarianization of geographically differentiated populations which it has to compel to commodify their labor-power, and in actual history this process legally, politically, and ideologically involved the formation of racial categories

These are matters of historical fact, which we produce abstract concepts to grasp and understand. We cannot deduce the relation between "racism and capitalism" as pure abstractions, whether we want to claim that they are necessary to each other or not

The claim of necessity is generally an attempt to guarantee a political perspective with social analysis (since we're against both racism and capitalism, they are necessary to each other; or we think racism isn't as important, so it's not necessary). This is fallacious reasoning

Those who want to read more may be interested in Stuart Hall's "Race, Articulation, and Societies Structured in Dominance." I've read the other sources people have recommended, thanks, but this is the closest to my methodological perspective. https://rbb85.files.wordpress.com/2014/08/9a-hall-race-articulation-and-societies-structured-in-dominance.pdf