I think "moral realism" is a bad name for, well, moral realism. It gives the impression that to deny it is to deny that morality is "real."
But this conflates two things: whether morality exists, with whether morality has the specific qualities "moral realists" think it has: namely, that it consists of stance-independent moral facts.
It's misleading to imply that denying this entails that you deny morality is real, or that you're an "antirealist" about morality. I'm only a denier of stance-independent and irreducible normativity, not the existence of morality or of norms more generally.
I think moral realism benefits from undeserved appeal in virtue of its name alone. And I think framing philosophical disputes in a way that privileges some positions over others merely in virtue of the labels used to refer to them is a mistake.
Imagine if we called A-theory of time the "antiphysics theory of time" and B-theory of time the "consistent-with-physics theory of time." That'd be obviously partisan.
I think "moral realism" is a tendentious label from the outset, and that we could devise more neutral and descriptively accurately labels.