If you use any commercially-available cosmetic or personal care product - and you're in the VAST minority if you don't, you might want to read this post. Cosmetic preservatives are not a "nice to have", they're a must. Toxins be toxic, peeps, and the only way to keep them out of hydrous (water-containing) products is by preserving those products. (Note: those oil-based products can be as natural as natural gets - that's why I love them so and sell them!!)
There are no proven, all-natural preservatives on the market at this time. That's not to say that there are no natural options or that they definitively don't work, but they're not well-studied (potentially cuz there's no profit in it for the Man, I realize). FYI, the leucidal preservatives (relative market newbies that are made from plants and are on the more natural end of the spectrum) have a pretty bad rep and you need to use them in very high concentrations, by comparison with the synthetic versions.
What I didn't realize till recently is that many commercial "natural" brands hide their preservatives in the ingredients list under the INCI nomenclature "Fragrance" (which is a preservative containing product).
You often can't see or smell mold and yeast and fungus and gram negative bacteria in a hydrous product until they're rampant (and sometimes not at all). But put a sample under a microscope and it's a horror show!
I'm not going to suggest that test-tube cosmetic preservatives are something you'd want to eat. I'm certainly advocating that they be used in the recommended volume (which is always a very small amount). I stay away from the ones that seem unnecessarily evil (those containing parabens), though I'm not a scientist - so I read and make my determinations at a layperson level. It is possible that Big Cosmetic Pharma is fucking us over. But it's absolutely certain that nature will, if we use an unpreserved hydrous product more than 3 days after it's made.