If you believe in inalienable human rights, you can't be a moral relativist. A moral relativist holds that all moral obligations are derived from the norms of a society. But a right is a special kind of moral obligation, an obligation not to deprive you of something (life, liberty or the pursuit of happiness). Jefferson said that these come from our creator, which means that a society can't take them away just because it doesn't recognize them.
Of course if there is no creator, you have to rethink where those rights come from. Putting evolution in place of the creator creates this howler, which I gave in one of my first posts to this blog five years ago:
We hold these truths to be self-evident, that all men have evolved equally, and that they are endowed by Evolution with certain Inalienable Rights, that among these are Life , Liberty, and the pursuit of happiness.
Though this may be a special case of the issue of atheism and objective moral values.