My guess is that racism is driven by class war, so, like sexism or other forms of oppression, it's not _necessary_ to a class system but is very likely to appear.
However, suppose racism _is_ directly necessary to US capitalism. That does not mean that the particular segment of the bourgeoisie responsible for running General Motors are aware of the fact, or, even if they are, that they believe that Affirmative Action reduces racism or race conflict. Or, they may believe that the present level of racial conflict is an _embarras_de_richesses_.
I have read that large corporations have given substantial sums of money to fight anti-immigrant legislation and school vouchers (which generally seem to have a racial subtext). I myself in days of yore was sent by a large corporation to recruit the poor and differently pigmented even before the government rewarded such things; so General Motors' brief is nothing new.