Not at all. On some objective universalist level, moral relativism is right. Where it's dead wrong is that we should stop defending our way of life and our moral codes. We all have our own moralities and seek to shape the world according to it.

As an side, capitalism is more effective at achieving socialism's moral ends than socialism is. It's something people should get behind even if they don't place moral value on private property. You might disagree, but we can argue about that on the level of facts.