Some people are terrified of non-realist positions on morality. The reasoning goes as follows: if there is no objective morality, then what makes ISIS wrong? Why can't we behead people, or vivisect babies in a bathtub? Shouldn't there be some sort of objective standard that we can use to prove, on a rational basis, what is right and wrong?
On the one hand, I sympathize with the sentiment, but on the other hand, I think it is misguided. First of all, of course, the fact that something doesn't sit with us emotionally doesn't mean that it's not true. But I'm not even sure that the concern itself is well-founded. Consider: do you think that, if you were to engage an ISIS member in a levelheaded conversation about morality, you would be able to convince him that <insert your favorite moral system here> is the objectively true moral system, and not radical Islam? Radical Islam (like most religions) also has a realist understanding of morality, and their realist interpretation includes beheading infidels. So in order to convince them to adopt your realist system, you'd have to convince on the basis of...what, exactly? If you don't have a shared moral epistemology - that is to say, if you don't agree on a way to discover objective moral truth - then there's no way to convince the ISIS member not to behead people.
The worst case scenarios of non-realist views of morality, I think, are far less scary than those of the realist views. If no one believes in objective morality you tend toward an Ayn Rand-type world where everyone acts in what they believe to be their own self-interest. While it is possible to get stuck in suboptimal equilibria here and have complete anarchy, it's also quite likely that - without any moral realism anywhere - people will cooperate and create prosocial social norms which people perceive to be in their self-interest. And people can also be motivated - simply via self-interest - to create a government that passes laws, again for the common good. You can have strongmen who act in their own interest to harm everyone else, but in the long term the strength of numbers will always overpower the strength of a single person. And when the people don't overpower the strongman, there's often some sort of realist ideology (e.g. communism) which is preventing the natural emergence of opposition to an individual who ruins things for everyone else.
The worst case scenario for realist views of morality are far more scary, especially when there is no agreement on moral epistemology. That's how you get ISIS.
Societies have become less cruel over time (if you are of the view that things are getting better) not because we have discovered better moral principles, but simply because - via trial and error - we have figured out systems and social contracts that are more suited to people's preferences, and because people have figured out how to effectively utilize their power in numbers in order to acheive the preferences of the masses.
What about the individual? For the most part, if you live in a healthy society, social norms and laws will be sufficient to ensure that the individual behaves himself. The incentives in the system should be sufficient, in 99% of cases, to constrain individual behavior to be prosocial. And in the other 1% of cases, people will have to contend with their own conscience. But there are almost always consequences to anti-social behavior. Eventually.
