Absence of good and evil, design and purpose does not imply moral relativism. Anyone who comes to such conclusion has a flaw in their logic. Or they don't know the nature of consciousness.
I subscribe to Modern Synthesis and beyond, that is, theory of evolution and everything that's built upon it, and I'm not a moral relativist. It's simply because I understand that in this causal universe (causality really cannot be argued on a macro-level), there are only causes and effects. No labels of good and evil.
Some causes simply result in pain. A sensation which, in itself, is not evil. Subsequently, it's always I who's subject of/to all experiences. Pain included. Thus what you call morality is embedded in the very structure and behavior of nature.
Simply speaking, if you want to know yourself, you must behave in a way that minimizes pain in order to have the peace of mind needed for such endeavor. Conversely, if you know who you are, you behave in a way that minimizes pain because you know that every subject is identical. It's simple as that. So yes, moral relativism is BS, but your arguments why it is so too.