There's a good article in Jacobin: Why the Right Loves Privilege Politics.
First, one fundamental characteristic of capitalism is cutthroat winner-take-all competition: "winning isn't everything, it's the only thing." The marginal value of one more point (e.g. one more dollar) is usually negative; however, the marginal value of the winning point is the whole prize: the winner gets everything, and the loser gets nothing. The trouble is, we don't know what the winning point is until the game is over, so we have to fight to the death for every point.
Not only that, but being in the lead confers an advantage. First, there's the gambler's ruin property of statistics: in an interated fair game that's played until one player goes broke, the player with the larger bankroll has a larger probability of winning everything, even though each iteration is perfectly fair (zero expected value for each player). Second, there's the meta-game advantage: if the players make the rules, and the player with the most points/money gets more say in the rules, then players can use a slight advantage to tilt the rules in their favor.
In the context of cutthroat winner-take-all competition, even a tiny advantage is momentous. Regardless of whether the advantage really is "fair" or "unfair" (even granting that "really fair/unfair" is even a coherent concept), it pays to fight to the death to both obtain for one's self or negate for others the tiniest advantage, by any means possible.
Second, historically, capitalist competition has used sex, race, religion, gender, sexual orientation, physical (dis)ability, etc. ad nauseam to confer competitive economic (dis)advantage, and therefore political, social, and cultural (dis)advantage. It doesn't really matter to this analysis whether or not capitalist actually created these distinctions; what matters is that sex, race, etc. has been used for so long to construct competitive (dis)advantage that they are baked deeply into capitalism.
Thus, an important conclusion follows: We cannot eliminate sexism, racism, etc. unless we eliminate capitalism.
I want to be crystal clear about what I am not saying here. I am not saying that if we eliminate capitalism, we will automatically eliminate sexism, racism, etc. And I'm not saying that, within a capitalist system, it is pointless to ameliorate excessive sexism, racism, etc.
I am saying that if the goal is to eliminate sexism, racism, etc., then at some point we will have to eliminate capitalism, and replace capitalism with something (i.e. communism) that is not fundamentally based on cutthroat winner-take-all competition.
A corollary to the above: Even if capitalism were perfectly "fair," it would still be bad.
The fundamental problem is not that capitalism has sexism, racism, etc..* The problem is that cutthroat winner-take-all competition, even if it is perfectly fair, is bad in and of itself.
*Again, I'm not saying that sexism, racism, etc. are not problems; I'm saying that they are not fundamental problems.
I personally use utilitarianism as an ethical framework; therefore, by "bad", I mean that capitalism, and any other cutthroat winner-take-all competitive political economy, increases the suffering of the many for only the most dubious happiness of the few. But that even perfectly "fair" capitalism is bad is not particularly sensitive to one's ethical framework. Indeed, the only ethical framework I can see where capitalism is good is a framework that presupposes the value of cutthroat winner-take-all competition.
The point is, rather than fighting to the death about every small (dis)advantage, we should create a system where every small (dis)advantage is not potentially a matter of winning or losing, of life or death, of dignity or degradation. Dignity, happiness, satisfaction, well-being belong to everyone, not just to an ever-narrowing circle of "winners". When small (dis)advantages are no longer momentous, perhaps then we can work more calmly to actually eliminate them.