ugh.
First of all, the benefits of wearing sunscreen far outweigh the the dangers of using 'chemicals' on your skin. There is no evidence that the chemicals used in sunscreens cause cancer or other illnesses. There were some concerns raised over the use of retinyl palmitate, a form of vitamin A (which is also added to low fat dairy products) and oxybenzone on labatory rats but it was concluded that neither substances were toxic to lab rats or humans (
source)
Secondly, 'chemicals', and by that I'll assume you mean synthetic chemicals, are not inherently bad for you nor are 'natural' i.e. naturally occurring substances, automatically good for you. I mean, Poison Ivy is natural but good luck if you decided to rub that all over your face.
Any chemical used in sunscreen that has been produced or sold in the EU, USA, Australia etc will have been approved by the FDA, EU (or other governing health body) as a safe and effective sunscreen ingredient.
If you are going to judge the safety of a substance based on how pronounceable the name of it is make sure you avoid these scientific sounding ingredients: Butyrospermum Parkii, Simmondsia Chinensis and Persea gratissima*
It's unrealistic to expect people to avoid walking in the sun and actually its not good for you. Scientists say that regular small amounts of exposure to the sun is vital for the bodies ability to produce Vitamin D, a substance which is necessary to absorb calcium and form healthy bones. This is especially important for babies and children so as to avoid
Rickets. While you can take Vitamin D suplements orally there is a danger of developing hypocalcaemia and studies have also shown there are other related toxic side effects of taking supplements
source
Umbrellas and clothing do not provide adequate protection from the sun. They only prevent the wearer from direct sunlight, not the ultraviolet rays reflected from the ground.
Although sunscreen ('chemical' or otherwise) does not provide 100% protection, they do significantly help to protect against the damaging effects of the sun by reducing the amount of ultraviolet reaching the skin.
Protecting yourself from developing skin cancer or other illnesses should be higher on you list of priorities than ageing. If they aren't, have a word with yourself.
I thank you, and goodnight.
*thats Shea Butter, Jojoba Oil and Avocado Oil to you and me.