Actually zinc oxide is a mineral; iit is NOT a chemical!
Some sunscreen formulations include zinc oxide as an ingredient along with a sunscreen. Alone, zinc oxide is just a physical blocker of UVB and UVA rays and a mineral, organic compound. Natural elements can cause cancer too.
Zinc oxide is believed to be safe, but this is mainly because it does not penetrate the skin and sits on top of it. That is how it works - by "blocking" rays. Sunscreens work by absorbing rays and releasing the energy ater they are filtered. Because sunscreens are absorbed into the skin, there is some controversy of them causing cancer. But usually these studies involve testing if they are able to reach the blood supply - most cannot. A few can. Mexoryl, Avobenzone and I forget the other name (starts with an O, but there are many) are believed to be safe. These are mainly UVA filters used in a sunscreen mainly. In combination with a physical blocker such as zinc oxide or titanium dioxide, they offer more full range protection and photostability.
Sunscreens are not inherently "bad" because of the cancer claims. They offer better protection than pure physical blockers in general. Chances are if you are using a product that is more or less cosmetically appealing, it contains a sunscreen. This also means that you will need to reapply after two hours in direct sunlight to maintain the protection. Zinc Oxide is a better physical blocker than Titanium Dioxide in general, but I don't know many people who want to walk around with a white mask on their face.