Moral relativists don't believe that all positions are equally valid, my position is the most valid obviously. They believe moral positions are subjective.
Moral relativists can have moral beliefs. They simply recognise that these are their own (very strongly held) opinions, rather than a reference to a universal moral code (like say, the Ten Commandments)
I think the point is that if you're a moral relativist across the range of morals encountered in human societies you're hardly a moral relativist at all because from the space of all possible moral positions you've accepted as equally valid the tiny subset that have organically originated from the extreme restraints of human culture. It's far rarer to see moral relativists for example who think the moral positions of serial killers and humanitarians are equally valid, but even that range is small across the landscape of all possible moral positions.
Moral relativism is the view that ethical standards, morality, and positions of right or wrong are culturally based and therefore subject to a person's individual choice. We can all decide what is right for ourselves. You decide what's right for you, and I'll decide what's right for me. Moral relativism says, "It's true for me, if I believe it."
The vast majority of philosophers don't believe in moral relativism. It's actually usually the amateurs early mistake and you can read alot of the critique of it easily online.
You make a fact-like statement for what is actually one of the most debated arguments in philosophical history. I disagree, morality is subjective. http://en.wikipedia.org/wiki/Moral_relativism
Moral relativism is the most absurd form of moral realism, which is itself an absurd position. I'd be more interested in an explanation for why so many otherwise intelligent people, who are more than capable of reasoning for themselves and holding well-defended, sensible positions, find themselves attracted to moral realism, a truly mystical belief that offends science, reason, and grade school grammar.
Moral relativism is simply accepting that there's no value system that is rooted in immutable laws of nature - it's all cultural. It doesn't mean that you can't prefer one value system to the other, and make judgments accordingly.
That's not moral relativism, that's epistemic anthropocentrism (i.e. good and bad and all value judgements in general are made by humans exclusively using human terms of meaning and human perceptions).
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