I think Thomas Nagel is correct when he claims in "Subjective and Objective" (and also in his book, The View from Nowhere) that progress in science often takes the form of moving from a subjective or perspectival view of the world, to an ostensibly objective framework, in which the perspectival view is one among many other such views, and which accounts for why that perspectival view appears as it does.
We see the sun rising now. Problem is, people to the East saw the sun rising earlier. Did it, then, both rise and not rise? The difficulty is solved if we say that in fact the earth is turning, hence people in different longitudes see the sun cross the horizon at different times. That the sun 'rises' is perspectival; that the earth turns is (ostensibly) objective.
Similarly apparent versus absolute magnitude: I see the penny as an ellipse stretched out from North to South. You, at a right angle to me, see it as an ellipse stretched out from East to West. By supposing that, objectively, it is circular, and by supposing, too, the principles of optics, we can explain why it looks the way it does to each of us.
Heracleitus is clearly concerned these sorts of issues, with whether there are any claims that are non-perspectival: he suggests that predications (many? most? all?) which appear to be absolute are in fact perspectival because relative to some implicit class of comparison. Sea water is foul and fresh water healthy-- to us, of course; but to fish it's the other way round. Helen is beautiful--that is, only so long as we do not compare her with a goddess. (And yet, one might wonder, what about the claim, "A goddess is beautiful"? Is that similarly perspectival? What could show that claim to be true only relative to some class?)
Suppose we take Xenophanes to have a similar concern. There is a fragment which suggest that he does:
If god had not made yellow honey, men would consider figs far sweeter.
ei) mh\ xlwro\n e)/fuse qeo\j me/li, pollon\n e)/faskon
glu/ssona su=ka pe/lesqai
If he does have this concern, then we might plausibly take him to hold, furthermore, that remarks about gods cannot in this way be perspectival. In the theological fragments, then, he would be arguing, in effect, that the gods do not have bodies, on the grounds that any attribution of bodily form to the gods is evidently perspectival. His theological views would then become important because, like Milesian cosmology, they would be an example of someone's insisting upon the shift, so important for scientific progress, from a subjective to an objective point of view.
Now I am not proposing this, so far, as an interpretation. My point here is merely to sketch an interpretation which seems interesting and which has some plausibility, but which we wouldn't even happen upon--we wouldn't think we needed to formulate it-- once we had applied the crude 'reason/authority' distinction in interpreting Xenophanes.