Also, saying that there is one system of inequality doesn't mean there aren't others. Class is certainly another, related, system. But one doesn't reduce to another.
Yes it does. Every day I see people far more affected by class based inequality than race based inequality. Right now not having money would affect you far more than being a different race than you are.If you suddenly became a different race overnight chances are your life really wouldn't change that much, if you lost your job and all your money you'd be totally fucked. That means by definition one has a higher impact on the world.
It sounds like you're saying that one is more important. I honestly don't know whether class or race-based inequality is more of a problem; I think it depends on context. Both of them have caused great problems. I will point out that many people have been as "fucked" as imaginable for being labelled as a particular race: murdered, enslaved, forcibly displaced from their homelands, etc. And this sort of thing continues to this day, e.g. in Myanmar right now the Rohingya are arguably being genocided. If one of those people could change their race, they would be decidedly unfucked in that context.