I'm not a fan of sunscreen either. I can only imagine the long term affects the chemicals will have absorbed into my system.
I guess I'm one of the lucky ones....once I get a base I rarely burn from "long sun exposure". That said, I try to cover up with clothing and will dab some sunscreen on the back of my neck, ear tips and nose.
If I'm riding in humid weather I prefer cotton based shirts vs synthetics (feels clammy when damp)