You are right that my pithy summary was misleading. This may be a terminological point, but I am confused about how a hard-core scientific anti-realist can believe in predictions. At the very least, someone who thinks there is no objective physical reality has a hard time explaining why science seems like a one-way ratchet, with predictions always getting better and never getting worse.

I agree that science, like all facts, are socially-mediated. I think the case for incommensurability between certain scientific theories is overwhelming. But it seems like there must be some regularity external to human minds for scientific predictions to work the way we've observed them to work. (I vaguely recall my Philosophy of Science professor saying something like "Preserve the phenomena")

In short, the problem of Induction says that we can't prove the sun will rise tomorrow in the sense that we can prove that 3 + 5 = 8. But hardcore scientific anti-realism proponents seem like they should be surprised when the sun rises tomorrow (more precisely, when they experience what appears to be the sun rising tomorrow) because they literally believe that there is no mechanism that suggests it will happen. (Or am I just setting up a strawman?)

I like your explanation of the distinction between (metaphysical) skepticism and anti-realism. Another way of putting it would be that the for the skeptic, the standard to evaluate beliefs/theories is correspondence with objective reality, but they also believe that there is no reliable way to compare map and territory and therefore all our beliefs are unreliable. The anti-realist denies objective reality is a meaningful concept, judges beliefs by some other standard like consistency or pragmatic usefulness, and if happy to endorse them if they satisfy it.

Or as Thomas Nagel memorably put it in this passage from The View From Nowhere, epistemological theories can be classified as skeptic, reductive (meaning not "reductionist" but "anti-realist"), or heroic:

Skeptical theories take the contents of our ordinary or scientific beliefs about the world to go beyond their grounds in ways that make them impossible to defend against doubt. There are ways we might be wrong that we can’t rule out. Once we notice this unclosable gap we cannot, except with conscious irrationality, maintain our confidence in those beliefs.

Reductive theories grow out of skeptical arguments. Assuming that we do know certain things, and acknowledging that we could not know them if the gap between content and grounds were as great as the skeptic thinks it is, the reductionist reinterprets the content of our beliefs about the world so that they claim less. He may interpret them as claims about possible experience or the possible ultimate convergence of experience among rational beings, or as efforts to reduce tension and surprise or to increase order in the system of mental states of the knower, or he may even take some of them, in a Kantian vein, to describe the limits of all possible experience: an inside view of the bars of our mental cage. In any case on a reductive view our beliefs are not about the world as it is in itself – if indeed that means anything. They are about the world as it appears to us…

Heroic theories acknowledge the great gap between the grounds of our beliefs about the world and the contents of those beliefs under a realist interpretation, and they try to leap across the gap without narrowing it. The chasm below is littered with epistemological corpses.[1]

[footnote 1] A fourth reaction is to turn one’s back on the abyss and announce that one is now on the other side. This was done by G.E.Moore.