By way of analogy, consider what is the practically rational response when we learn surprising things about the world, such as the fact that apparently solid objects are mostly empty space. It seems to me perfectly practically rational to act as if such objects are as solid as they appear, and to feel trusting in their apparent solidity, even if, when I reflect, I don't believe that they are solid (at least, not in the way they appear to be).
Imagine an old-school model of a salt crystal, a little cube, made out of little spheres of various sizes connected with little rods of various lengths. Is it solid? One way of taking the question is: are the components solid, as opposed to hollow: are the spheres more like ball bearings or table tennis balls; are the tubes dowels or pipes. But perhaps that's not what's meant; what's meant is: is the whole assembly solid. In that case, I find myself uncertain how to answer: what is meant by solid, in that question? Solid as opposed to what? But I might accept the following answer: construct the smallest (geometric!) solid that entirely encloses all the spheres and rods and whatnot, and observe that it's not the same stuff all the way through; it is, in fact, mostly air. Conclude, then, that it isn't solid, even though it's not quite right to say it's hollow or something like that either.
Perhaps something like that would underlie the assertion that "apparently solid objects are mostly empty space"; sc. merely apparently solid but actually not (or there's no point in mentioning it). A (merely) apparently solid iron cube, 1cm on a side, actually is not solid, being mostly empty space. Now there are some applications in which we would indisputably be justified in treating the cube as being "as solid as it appears" (more on which soon); for instance, we might calculate from its volume of one cubic centimeter and iron's density of so and so many grams per cubic centimeter that it has a mass of so and so many grams. This is perfectly in order; we aren't imagining that the cube fails to be solid by failing to be solid iron, that is, by being an iron exterior with an interior of copper, or air, or whatever. Our concern is one that would attach to the iron exterior, too; it too would really be mostly empty space. And this means that the suggestion that the cube isn't really solid itself doesn't affect the propriety of our calculation in the way one might have expected. The calculation that the cube is so and so many grams might be understood to be approximate on the grounds that, for instance, it probably isn't 100% pure iron. Maybe there's even a pocket of air in the cube! That would mean that we wouldn't be getting the right answer from the calculation, because of the non-iron in the cube. But in the ideal case where none of that happens, we aren't in danger of getting the wrong answer on the grounds that the cube isn't really solid, because the figure for density is derived from iron which is similarly mostly empty space—that's what solid iron is.
What is the solidity that the iron cube lacks? Is it that it's not the same thing all the way through? But isn't it?—assuming it's pure iron, isn't it iron all the way through? And the purity of iron isn't impugned by the fact that a chunk of the stuff has, in addition to atoms of Fe, space between the atoms of Fe. "Stuff" used advisedly in the previous sentence: the idea that a piece of iron isn't the same all the way through seems to come from an opposition to the idea of stuffs of things, as if iron, or anything else, could only be solid if the atoms were literally adjacent to one another. Though it's not clear what that would mean. After all, the atoms themselves are mostly empty space, too, right? The electrons aren't all touching the nucleus. (It's also not clear, actually, that one can't say that it's composed only of all the same thing, namely, Fe atoms. The empty space isn't an ethereal entity that also comes into the composition!) What, for that matter, is the solidity the iron cube appears to have? It looks impermeable by raisins; does it look impermeable by neutrinos? Or is it just that—in contrast to puffy gribenes—it looks as if it's not mostly empty space? (But then the puffs in the gribenes don't look as if they're empty space, they look like air bubbles. Air is also mostly empty space in the same way that iron is, but it doesn't look that way, does it?) It seems odd to say that it looks as if it has the solidity that would come from being nothing but Fe nuclei right next to each other.
"I don't believe they are solid (at least, not in the way they appear to be)" undermines itself: there doesn't seem to be another coherent way for them to be solid. On initial reflection, one may be inclined to say that cubes of pure iron aren't really solid, since they're mostly empty space; further reflection ought to lead one to the conclusion that that's just part of what it is for iron, or anything else, to be solid.