To wake up as a villain
One common objection or concern with relativism and antirealism more generally is that the relativist could just wake up tomorrow and desire to torture or kill people, and then be perfectly okay with committing such actions.
This strikes me as quite a bizarre worry. The fact that a relativist’s moral standards may be contingent by their own lights does not in any obvious way make them any more unstable than the realist’s moral standards; the difference is simply what it is that’s unstable.
The relativist could wake up and decide that it’s consistent with their standards to torture and kill people, and therefore decide that it’s morally permissible to do so.
But a realist could wake up and believe that they have an objective moral obligation to torture and kill people, and therefore decide that it’s morally permissible to do so.
If our concern is with moral judgment and behavior, it’s not obvious why we should think changes in fundamental standards and values should be more unstable than beliefs about what’s objectively morally permissible or impermissible. The former might even be more stable than the latter: it's a lot more difficult for me to change my preferences than my beliefs.
My food preferences have barely changed through my entire adult life. Many of my other preferences have likewise remained stable. And some have remained static: I care more about my friends and family than other people. I don't think I could just decide on a whim not to. If anything, my moral values seem even more stable. I can’t just voluntary choose to be okay with torturing babies or killing people for fun. At the very least, it’s not obvious that I can do so, or that if I tried, that it’d be easy.
On the other hand, I’m not at all convinced that it’s much more difficult to convince a moral realist to change their normative moral beliefs, that is, to change what they think is objectively morally right or wrong. Indeed, I suspect if we conducted a survey, we'd find that moral realists change their normative moral beliefs more often than antirealists change their fundamental values and preferences. This is an empirical matter, of course, but I'm willing to bet that moral realists have less stable moral commitments than antirealists.
The presumption many people have is that belief in moral realism somehow insulates you from the risk of deciding that it’s consistent with your subjective moral standards to commit atrocities. I question this presumption. On the one hand, if the moral realist wouldn’t commit “atrocities” (understood in some descriptive, nonmoral sense, e.g., torturing babies) because it’s inconsistent with their subjective goals, standards, or values, then the reason they’re insulated against committing atrocities isn’t because of their commitment to realism, but because of their standards.
If, on the other hand, they are motivated to comply with whatever the objective moral facts are, then a realist may be inclined to commit atrocities (e.g., baby torture) regardless of whether it’s consistent with their goals and stand standards to do so; alternatively, the goal or desire of a moral realist to act based on whatever they think the objective moral facts are could cause a moral realist to desire or develop the motivation to commit an atrocity precisely because they believe it’s morally good or permissible to do so.
In other words, while realists may worry that antirealists may decide it’s consistent with their subjective preferences to commit atrocities, and that a commitment to antirealism opens the door to potential atrocities, there may be a parallel set of reasons to worry that moral realists might be receptive to committing atrocities that isn’t available to the antirealist, because the antirealist has no interest in complying with whatever the objective moral facts are; the realist, in contrast, is vulnerable to committing atrocities due to the mistaken belief that it’s objectively morally good or permissible to do so, even if it's inconsistent with their preferences/desires.
In short, moral realism may be just as capable of motivating atrocities as antirealism; it’s just that such atrocities would be mediated by epistemic errors (false beliefs about what the objective moral facts are) rather than changes in subjective moral standards.