One way to answer this question, I think, would be to consider the history of science. Ptolemy, for example, believed that the earth was at the center of the universe, and that the sun and other planets revolved around it in roughly circular orbits, except for "eccentricities" accounting for which was much of what astronomers did in those days. Copernicus corrected part of that, holding instead that the sun was at the center of the universe and that the Earth and other planets revolved around it, with only the Moon (now not considered a planet) revolving around the Earth. But Copernicus too thought that the orbits of the planets were roughly circular, except for eccentricities
By the time of Descartes, it was realized that the sun is not at the center of the universe, but it one star among many, though Descartes did think the sun was at the center of (what we would now call) the solar system. Kepler would later replace the view that the orbits of the planets are circular with the much more nearly correct view that they are elliptical and place the sun at one of the foci of these ellipses. Newton would then show how Kepler's equations can be derived from more fundamental laws of physics, showing that the orbits are not perfectly elliptical, (since the planets exert a gravitational force on each other. The sun then doesn't occupy a special place at all, even in the solar system. If anything does, it is the center of mass of the solar system.
But then it turned out that Newton's account couldn't explain the so-called procession of the perihelion of Mercury. It's inability to do so is part of what led to Einstein's discovery of relativistic physics, which does explain it and brings us to the present day.
Now, it seems to me that we must surely regard all of these views as reasonably held. It would, of course, be utterly unreasonable for me or you to think that the Earth was at the center of the universe. But it was a perfectly sensible thing for Ptolemy to think, and the theory in which this belief was embedded was actually pretty successful, as theories go. The same goes for Copernicus's view, Kepler's, Newton's, and Einstein's.
And that, I think, is the key here. It is not so much views that are reasonable or unreasonable. Views can, rather, be reasonably or unreasonably held. That is, one may good reasons to hold those views, have taken proper account of all relevant and available evidence, and so on and so forth. So "reasonable", in this use, is an epistemic adverb, and of course false views can be reasonably held. Surely it is now reasonable for you and me to believe the relativistic account of the orbits of the planets. But some hot-shot physicist may yet come along and show us that we believe falsely.
That said, philosophers do sometimes describe other philosophical views as "reasonable". What they mean, I think, is that someone relevantly like the people engaged in whatever discussion is underway might reasonably hold that view. I.e., that merely holding the view doesn't indicate that one is failing to take proper account of relevant evidence or otherwise being irrational.