Yes it does strip the oils, but a proper bar of soap deposits glycerin which acts as a humectant in the same way that those oils do. I've made my own bar soap for many years now and the only dry skin problems I get is the skin on my shins drying out during winter months -- an area that I don't actively wash with soap.

Homemade or clasical bar soap contains glycerin naturally. Commercially made bar soap usually has the glycerin stipped out because they can resell it at a much higher price in cosmetics and skin care products.