Edward Feser at Right Reason distinguishes between two kinds of libertarianism (though he later doesn't think they're both equally worthy of the name), the kind that favors free markets and limited government and the kind that goes much further and requires government neutrality (as opposed to presumption one way or the other) on every controversial moral issue. Having made that distinction, he goes on to explain why he thinks the latter view is morally deficient:
If "libertarianism" is merely another way of describing the classical liberal presumption in favor of free markets and limited government, then it is a healthy tendency which conservatives ought to welcome. But if libertarianism entails also that government can and must be neutral between views about the moral legitimacy of abortion, same-sex marriage, and euthanasia; that we can have no enforceable positive obligations to other human beings other than those we explicitly consent to take on; and that a society can be perfectly just as long as property titles are respected, no matter how morally depraved that society might otherwise become, then it is a view that is in my estimation false and dangerous, and ought to be opposed by every conservative.
This doesn't quite map onto my distinction between two kinds of libertarianism I've talked about before, but that's because it focuses on one of them as wrong and then offers an alternative that seems to avoid both problems. The key to his view is to insist on some moral principles, even controversial ones, that the law needs to enforce, all the while presuming in favor of limited government and free markets. That's consistent with also presuming in favor of views that are traditionally conservative, and his way of doing that is taking somewhat conservative views on abortion, euthanasia, and gay marriage.
I'm not interested in the details right now except to note that this is a kind of libertarianism that is neither of the two that I think have obvious problems. We might call one moral skeletal libertarianism. Some libertarians think the only true moral principles are the ones they're willing to enforce, and they take this so far that they don't think we can ever acquire a positive obligation toward someone unless we do something to acquire it. We have negative obligations, because those are grounded in rights of other people that we don't do certain things to them, e.g. harm them, lie to them, steal from them. We don't have any duty to do anything for anyone. The clear counterexample is finding a baby on your doorstep as you return home one night. Anyone who doesn't think I have an obligation at least to do something for that baby is morally deficient. The skeleton of morality that this view recognizes is jaundiced enough that I have a hard time seeing how a healthy moral thinker can adopt such a view.
The other main version of libertarianism has a more robust moral framework than the skeletal version. The difference from political conservatism or liberalism is that those moral principles are worth enforcing only if enough people agree with them, which basically just amounts to second-order moral relativism. It's not relativism about the moral principles themselves but relativism about the second-order moral principles that determine which moral principles are worth enforcing. Those still moral principles, and if what people happen to believe determines wholly what those principles are I think it's worthy of the name 'relativism'. I call this moral wimpiness because, while there is a moral structure there, there's no desire to have it affect how anyone lives in relation to anyone else. A government can then be considered just if it allows all manner of things that are seriously wrong, simply because the government has no right to interfere in certain things. That's moral wimpiness. You believe something but aren't willing to act on it.
I think Feser's view avoids the charge of moral skeletivity, because he does take there to be true moral claims that are quite controversial. It avoids the charge of moral wimpiness, because it insists that some moral claims that are controversial are still worth enforcing. Is this still libertarianism, then? He suggests that it might not be. Maybe it's better to call it libertarian conservatism or something like that. I suppose there could be libertarian liberalism if you had libertarian principles grounding liberal positions on this issues he says you can have laws about that are controversial. I think he's right that this sort of view does support conservative views on abortion and euthanasia. I can see how his arguments on that will go, because I've made them myself. I'm curious why he thinks the same is true of gay marriage, though. His second post still hasn't gotten to the justification for these specific claims, focusing instead on smoking crack and prostitution, so I'm patiently awaiting more.