One question is what we want "morality" to refer to under anti-realism. For me, what seems important and action-guiding is what I want to do in life, so personally I think of normative ethics as "What is my goal?".

Under this interpretation, the difference between biting bullets or not is how much people care about their theories being elegant, simple, parsimonious, vs how much they care about tracking their intuitions as closely as possible. You mention two good reasons for favoring a more intuition-tracking approach.

Alternatively, why might some people still want to bite bullets? Firstly, no one wants to accept a view that seems unacceptable. Introspectively biting a bullet can feel "right", if I am convinced that the alternatives feel worse and if I realize that the aversion-generating intuitions are not intuitions that my rational self-image would endorse. For instance, I might feel quite uncomfortable with the thought to send all my money to people far away, while neglecting poor people in my community. I can accept this feeling as a sign that community matters intrinsically to me, i.e. that I care (somewhat) more strongly about the people close to me. Or I could bite the bullet and label "preference for in-group" as a “moral bias” – biased in relation to what I want my life-goals to be about. Perhaps, upon reflection, I decide that some moral intuitions matter more fundamentally to me, say for instance because I want to live for something that is “altruistic”/"universalizable" from a perspective like Harsanyi’s Veil of Ignorance. Given this fundamental assumption, I’ll be happy to ignore agent-relative moral intuitions. Of course, it isn’t wrong to end up with a mix of both ideas if the intuition “people in my community really matter more to me!” is just as strong strong as the intuition that you want your goal to work behind a veil of ignorance.

On Lesswrong, people often point out that human values are complex, and that those who bite too many bullets are making a mistake. I disagree. What is complex are human moral intuitions. Values, by which I mean "goals" or "terminal values", are chosen, not discovered. (Because consequentialists goals are new and weird and hard for humans to have, so why would they be discoverable in a straightforward manner from all the stuff we start out with?) And just because our intuitions are complex – and totally contradicting each other sometimes – doesn't mean that we're forced to choose goals that look the same. Likewise, I think people who think some form of utiltiarianism must be the thing are making a mistake as well.

However, the compulsion to bite bullets is at odds with moral anti-realism, another popular belief among EAs.

Well questions of how one ought to act are about ethics, while questions about the nature of morality are about meta-ethics. Meta-ethical principles can inform ethics, but only indirectly. An anti-realist can still have reasons to affirm a consistent view of morality, and a realist can still refuse to accept demanding forms of morality.

So is morality closer to physics or biology? An empirical approach to morality would view it as stemming from evolutionary psychology, social structures, and historical serendipity. Psychology, sociology, and history are some of the only fields even less law-like than biology.

Empiricist approaches to metaethics define morality as something to be learned from human experience. This is notably different from the process of scientific methodology which is applied to fields like psychology and biology, whether law based or not. You generally can't determine any facts about morality by studying its psychology, genealogy and history in society, as those refer to how people act and moral philosophy refers to how they ought to act. Some would argue for ways that you can derive normative conclusions from social science fields, although I believe those ideas are generally limited and contentious. Nevertheless, the nature of the fields' scopes and methodologies are entirely different, so I don't think you can draw meaningful parallels.

A popular bullet to bite is an argument of the form “X is theft/rape/murder”, where X is an act that is widely believed to be morally acceptable but that has superficial similarity to a serious crime.

I'm not aware of this being common. The LessWrong link doesn't seem to be relevant to legitimate moral philosophy. Can you give some examples?

Typically we are dealing with issues where the conclusions of a moral principle are highly counterintuitive. This can take many forms.

Morality becomes even more complex when it involves competing values. There is no inconsistency in believing that airports should X-ray luggage to reduce security risks and simultaneously believing that widespread surveillance of citizens is unjustified. One can value both security and privacy and believe that in some cases one outweighs the other. This point is often lost in bullet-biting morality, which views “inconsistency” as a product of hypocrisy and cowardice.

This is basically true (except that inconsistency is viewed as being irrational or wrong, rather than being slandered or denigrated) although typical utilitarian approaches also lead to similar conclusions about things with instrumental value such as privacy and security, while optimizing for multiple values can still lead to highly counter-intuitive moral conclusions. Mostly any aggregating ethic will have this feature. If we optimize for both autonomy and well being, for instance, I may still find it morally obligatory to do overly demanding things to maximize those values, and I may find cases where causing serious harm to one is worth the benefits to the other.

You can add more and more values to patch the holes and build a really complicated multivariate utility function which might end up producing normal outputs, but at this point I would question why you're optimizing at all, when it looks like what you really want to do is use an intuitionist approach.

Similarly, optimizing for naive definitions of utility will lead to paperclipping. For example, if we believe in one definition of utility, we may end up with a universe tiled with thermostats.

Yes, although most people, moral realists included, would affirm a fundamental difference between phenomenal consciousness and movements of simple systems.

Moral anti-realism doesn't like neat conclusions: though there's no reason to favor biting bullets, there's no reason to disfavor it either.

This is sort of true but, again, it is because meta ethics doesn't have too much to say about ethics in general. Moral realism also doesn't generally favor bullet biting or not bullet biting: there are tons of moral realists who favor intuitive accounts of morality or other 'softer' approaches. Moral principles don't have to be hard and inflexible; they could presumably be spongy and malleable and fuzzy, while still being true.

The rationale for the anti realist to decide how to face counterintuitive moral cases is going to depend on what their reasons are for affirming morality in the first place. Those reasons may or may not be sufficient to convince them to bite bullets, just as is the case for the moral realist.