I don't totally understand why people want everything to be "natural," other than because it sounds vaguely better than "unnatural," if you don't think about it too much. But some people do, so fine. If that's your thing, you should still wear sunscreen - and you're in luck because zinc oxide is pretty natural (though there is nothing wrong with chemical sunscreens - here's one I like). The downside is that zinc oxide tends to be quite opaque, so it can leave a white cast on the skin. Some formulas add tints or other active sunscreen ingredients to mitigate that whiteness, but then maybe it's not so natural anymore.
Other companies, like Jessica Alba's The Honest Company apparently just decreased the amount of zinc oxide in their "ultra-pure" natural sunscreen from 20% to 9.3%, because people didn't like the texture and appearance, while keeping the SPF 30 label on the bottle. Most other zinc sunscreens contain 18-25%. Keep in mind that the FDA has rules about SPF, but it relies on companies themselves to test their own products. The Honest Company says that they added "other ingredients" - unspecified - to compensate. But those other ingredient are not sunscreens, so they're not going to maintain the SPF. That's nonsense. And judging from consumer complaints, that solution did not work, because people have been getting literally burned by this shit.
So if you want all natural zinc-based sunscreen, you're going to have to compromise: either it's going to be less esthetically pleasing or less effective. Of course there are lots of great zinc sunscreens out there that work well, but they tend to have scary added "chemicals" (OH NOES) in them.
(Note: The Honest Company's sunscreen is marked Out of Stock on their website, so hopefully that means they have pulled it from their online store to reformulate.)