Anybody following current events or political philosophy is probably aware of the various gradations of "purity" in parties and movements. Among Libertarians there are those that are referred to as "Beltway Libertarians", "Left Libertarians" or "Randians" , etc.
A term I have never seen is "Atheist Libertarians", even though there seem to be quite a few - Rand, for instance - and many of them are the most libertarian of the bunch. This is a case of someone grounding his philosophy on feeling instead of principle.
If man has rights, they must originate somewhere. If there is no God, they don't originate with him who does not exist; therefore, they must originate with man. If there is no creator, man is an accident; he is not "endowed by their Creator with certain unalienable Rights." He is endowed with no more rights than a bacterium. Some people argue that rights originate in "nature." If this is so, where does nature obtain these rights and what are the consequences of their violation? How do we discover exactly what these rights are with which nature has endowed us? There are other explanations of where rights come from such as "society" or "the community" or government. These explanations don't work out very well for the obvious reason that if these entities bestow rights, they can just as easily and justifiably revoke them.
God might be viewed as the first and greatest libertarian. He gives man free will, but also a brief set of rules relating to his use of that will. Eighty percent of these rules are negative; "Thou Shalt not", steal, kill, lie, covet, etc. Only two are positive; Keep Holy the Sabbath Day and Honor your Father and Mother.
Jews, Christians and Muslims accept that these are divine commands, even if they have difficulty keeping them. From the standpoint of these religions, all the Libertarian arguments fall into place. This is not to say that all adherents of these religions are Libertarians, but to say that libertarian ideas are not incompatible with them.
The Atheist-Libertarian would probably argue that adultery is fine as long as no coercion is used - unless there is a breech of contract objection to it - and that there is no prohibition against strange gods, since there are no gods, strange or otherwise. As far as the Decalogue relates to the person and property of his fellow man, the Atheist-Libertarian would probably fall into line with orthodox practitioners of the three monotheistic religions.
The question is, on what basis are any of these things wrong in the absence of a divine prohibition? Why is it wrong to kill your fellow man, but not germs, roaches, poison ivy or kudzu? Why is it wrong to steal from your fellow man, but not from honeybees, sheep or silk worms? Don't animals have a right to the fruits of their labor? If not, why not? In the absence of God, how do we discover what kinds of things have rights and which ones don't? Is it wrong for the cheetah to kill the gazelle, or for the hyena to "steal" the gazelle from the cheetah after exerting all that effort? Doesn't the cheetah have a "property right" in the gazelle after exerting its energy and labor to kill it?
How can an accidental agglomeration of cells be said to have any "rights"? What can that possibly mean?
One person - group of cells - says that it has rights and another equally complex group of cells says no you don't. Neither can appeal to any higher authority than his own will.
There might be some argument advanced from practicality that society just works best when rights are respected. This still does not explain what rights are, where they come from, how we know what they are or what "works best" means; works best for whom? The only philosophy that seems to make any sense from an atheistic position was summarized years ago in a Schlitz Beer commercial that proclaimed, "You only go around once in life so you've got to grab for all the gusto you can." An appeal to hedonism, but if your life is like smoke, that is here for a little while and then vanishes, it's the only thing that makes any sense, instead of worrying about non-existent rights.