Moral relativism gets a bad rep, but let's take a look on what it actually means:
In philosophy moral relativism is the position that moral or ethical propositions do not reflect objective and/or universal moral truths, but instead make claims relative to social, cultural, historical or personal circumstances.
Now this stance is perfectly logical and reflects the reality of morals and ethics, because morals are in fact relative to social, cultural, historical and personal circumstances.
Unless you believe in God given morals and ethical standards, I don't see a strong argument in favor of the natural rights theory. Some proponents of the theory state that human nature is proof of the existence of these rights, and they seem to confuse what they think ought to be with what actually exists. This is known as the Is-ought problem.