Racism and sexism are primary means of class oppression in the US. The class oppressions you speak of were established and continue to be maintained that way. The racial and sexual bigotries of white men in the US have been the primary means of coordinating them in opposition to their class interests. Racism is not "secondary" to "class issues": it's one of their primary bases, most significant supports. Likewise sexism. Not "regardless". It discriminates in its "regards". It affects different races and sexes differently. That's how the Republicans get white men to vote for it.