No honest, reflective person would tell you that the relationship between race and class, or gender and race, etc. was a simple and straight-forward matter. It doesn't mean that there aren't better and worse views about how different oppressions are related to one another. It doesn't mean that there are "no right answers" here, or that things are so difficult that there's no hope of making headway. But it does mean that things are often more complex than a simple slogan or one-liner would have us believe.
Now having said that, I think there is something that should be extremely obvious, politically speaking, even in the absence of a fully articulated theory of how racial subordination, class exploitation, gender domination (and other modes of oppression) are interrelated.
In order to even be on the Left at all, you have to oppose unjust subordination and oppression wherever you find it. There is no excuse for anyone on the Left to be sanguine about racism or sexism. To be on the Left is to oppose class domination, sexual oppression and racism all at once, even if you lack a systematic understanding of how these are all interrelated.
Thus, there should be no confusion or hesitation about why Leftists must defend even people like Sarah Palin from sexist attacks. The reason is simple: the problem with Palin is quite obviously not that she's a woman, the reason to criticize her is that she stands for reactionary politics. Leftists cannot sit comfortably while she is criticized merely for her gender. To tolerate sexist attacks against her is to tolerate oppression, something no self-respecting Leftist could do.
Similarly, no Leftist could sit calmly while someone leveled racist slurs at Thomas Sowell or Michael Steele. Again, the problem with Sowell and Steele is that they are Right-wingers, not that they are black! No genuine Leftist could possibly sit calmly while someone called Sowell racist slurs. Confusing criticism of his politics with a criticism of his qua black person is an ugly mistake indeed, one which absolutely brushes entirely against the grain of what Leftist fight for.
Finally, consider a poor, White racist man. It is obvious that Leftists must criticize such a person for his racist views. Poor or not, racism as such can never be tolerated. But a Leftist should feel uneasy about criticisms of such a person which impugned him only insofar as he is poor. Snickering about holes in his clothes or his malnutrition is not material for a Left-wing critique. Likewise, it would certainly not be a Left criticism of such a person to say that his low wages and long hours at, say, Wal-Mart were entirely his own fault. The problem with such a person is just that he is a racist, and no apologies whatsoever should be made for criticizing him as such. No socialist would deny that sections of the White working-class have been quite racist and xenophobic indeed. What socialists could not tolerate, however, are bourgeois slanders to the effect that some are born to be poor and exploited and therefore deserve their lot.
Even in the absence of agreement on a systematic theory that explains the relations between sexism, racism and class domination, the need to avoid the above confusions should be obvious.