I hope you mean "if they are actually observed".

Yeah, that's it.

But, if we didn't believe (to a degree) in theoretical predictions before making observations to confirm them, then we wouldn't know what observations to attempt, and would almost never actually observe something useful!

The anti-realist doesn't say that we don't believe in theoretical entities. She says that we don't have strong reason to believe in them. I suspect most of us believe in things we don't have strong reason to believe in. It might be an anthropological fact that scientists tend to believe in theoretical entities and use these beliefs as guides to future research. Anti-realists don't want to deny this fact, they want to deny that the scientists' epistemic attitude (prior to making the requisite observations) is justified.

Anchoring on what most humans can observe unaided is just silly. I have acute myopia since age 6; without modern glasses I wouldn't be able to observe the moon in the sky - or to read about any scientific theories. Should I discount them on that account? Or if someone were born with unusually fine eyesight, making them the only person able to observe a tiny mote of dust - should everyone else disbelieve them? If a trained dog barks when he smells explosives, which humans can't smell, should we ignore the dog?

I agree. This is what I was trying to say when I said the distinction between observable and unobservable doesn't make sense. It would be silly to construe "observable" as "observable without technological aids", but once one allows technological aids, where do you draw the line? We have experimental verification of quantum chromodynamics. Why doesn't this count as (extremely indirect and mediated) observation of quarks?