I think you can be a moral realist and bite bullets too. If you accept some form of moral casuistry you needn’t have any moral laws at all, just a collection of judgements. But you can still be perfectly realist.
Of course, you are still right in this case. Anti-realists don’t need to bite bullets either. I have started wondering recently if I should be as neutral about biting bullets as I was (I just saw them as a way to ensure consistency). However really, they are occasions when intuitive morality which is the ultimate basis of my moral reasoning, disagrees with my conclusions. So perhaps, as you seem to imply, biting bullets should be viewed negatively (hence why some EAs find it off-putting, they already view it negatively).
I think you can be a moral realist and bite bullets too. If you accept some form of moral casuistry you needn’t have any moral laws at all, just a collection of judgements. But you can still be perfectly realist. Of course, you are still right in this case. Anti-realists don’t need to bite bullets either. I have started wondering recently if I should be as neutral about biting bullets as I was (I just saw them as a way to ensure consistency). However really, they are occasions when intuitive morality which is the ultimate basis of my moral reasoning, disagrees with my conclusions. So perhaps, as you seem to imply, biting bullets should be viewed negatively (hence why some EAs find it off-putting, they already view it negatively).