Well, when you are a moral relativist for one. The arguments for and against natural rights theory are long and intricate, so for this piece of commentary I will assume one is a moral relativist and explore how this would affect holding Anarcho-Capitalist principles.
The essence of moral relativism is that morality is subjective and hence an individual creation, be it through the prism of genetics and/or upbringing. Since all morality is derived from an individual perspective it follows that there can be no objective moral definition outside of the individual, in other words there are ethical systems intrinsic to us as subjective beings, but no independently verifiable moral code that we should follow. This point of view has some immediate benefits, the most obvious being that if morality is subjective there is no right to impose your version of morality on others. At first glance this all ties in well with the general consensus of Anarcho-Capitalist ethics, i.e. the principle of non-coercion and/or non-aggression.
Unfortunately it is not as straightforward as this. For example if morality is subjective an individual can, from their point of view, quite self-coherently create what they consider a set of moral absolutes. Then we are back to the situation of the potential imposition of morals with force, one of the hallmarks of the state. However, this situation can be avoided. This is so because it is still a logical truism to say that positive hypothesis need proving whilst negative hypothesis stand until a positive hypothesis can be verified to counter the negative situation. In more simple terms, the Anarcho-Capitalist does not need to acquire absolute rights to go about his or her business, but only to take the logically sound position that no such right exists to impinge upon their business until such time as a positive right can be objectively verified.
To my knowledge no one has ever conclusively verified a positive right and, as such, Anarcho-Capitalists can be moral relativists without accepting either the 'ethics' of those who wish to impose an absolute morality or those who in any other way act as if they held positive rights to another's liberty.