In a place such as SteemIt, where many libertarians freely exchange ideas, objective morality seems to be a given, while relativistic morality is considered a mental flaw. But rallying cries do very little for the discussion. Maybe moral objectivists will win the argument some day, but for this to happen, they should stop and listen to their opponents.
First of all, what does objective morality mean? What most people understand by it, is the position that morality is anchored on a set of universal principles and that we can use reason to derive from those principles how we should behave. (This is a common position among religious people, who think morality ultimately rests on divine revelation. For this article, I'll just ignore the religious side of the argument and deal only with the secular sort of objectivists.)
The problem with the objectivist approach is that, while you can use reason to derive ethics from principles, you cannot use it to get those principles in the first place. For example, you may say that “theft is wrong” and “taxation is theft”, then conclude that “taxation is wrong”. But why was theft wrong to begin with? Maybe because “injustice is wrong”, “theft is unjust”, then “theft is wrong”. This sort of regression is supposedly stopped by some universal principle but, whatever it is, it doesn't come from reason alone.
On a Ted Talk defending something akin to objective morality, Sam Harris argues that humans have a hardwired sense of morality that can effectively be used as principles for a rational morality. He's quite right about that – most humans (the exception being psycopaths) will naturally find that “reducing suffering” for example, is a firm basis for morality. But this doesn't correspond to what objectivists aspire. There's to reasons why: first because this hardwired principle is consequential in nature; and second because multiple principles can conflict with one another.
That leads us to a very important point that objectivists don't seem to address. Our morality is based both on principles, which is called deontological ethics, and on consequences, which is called consequentialism. Authors usually use deontological ethics to prescribe behaviors, but to understand how humans actually process morality, we must take consequentialism into account.
And what of consequentialism, then? The reason objectivists seem to avoid consequentialism is that it levels the playing field. Relativists, statists and many others make moral claims based on consequences while objectivist libertarians claim to use logic exclusively. But if you take consequentialism into account, than the objective claim “you can't tax in order to pay for the police, because taxing is itself an aggression” can then (in principle) be answered with “but if we don't tax, the absence of the police will lead to an increased overall rate of suffering”.
Consequentialism also allows us to deal with ethical conflicts. Imagine you are faced with a decision between two courses of actions, both which contradicts moral principles. Deontological ethics can tell you both are wrong. Consequentilism can tell you which is less wrong, allowing a practical decision to be made.
For a libertarian to say their view is the moral one, and be taken seriously, it is not enough to say their morality is internally consistent. Its consistency is not in question. He must instead convince the statist that the libertarian will provide the best consequences, which is much harder to do and much more relevant once it's done. Consequences are important. If you claim to be a libertarian and don't think the consequence of libertarianism is a reduction in suffering, I'd argue you may be rational, but is definitely immoral.
Leibniz once said that someday people would resolve moral conflicts by sitting down, taking an abacus and calculating the best course of action. Today, Sam Harris expressly says he doesn't think a computer will ever be able to tell right from wrong. The difference between these two is not that one uses reason and the other doesn't. It is because Leibniz reduced humans into little machines of logic operating under arbitrary premises. Sam Harris, on the other hand, recognizes a deeper dimension of humanity, and accepts the premises are contingent to the physical reality.
You read so far, you might find it interesting to read this article about religious morality, this article about deontologial and consequentialist morality and this article about objective morality.