What goes on my hair goes on my skin, I touch my hair with my hands, I apply products right up to the scalp, my hair sits against my face and neck when drying and so on. I'm more picky about what goes directly on my skin than my hair - doesn't have to be all natural, actually prefer short ingredients lists to numerous pointless plant extracts any of which might trigger a reaction.
I still like to avoid sulphate surfactants, silicones, mineral oil, parabens, colours and fragrances if I can. Sulphates damage my skin (atopic eczema/ contact dermatitis) and silicones just give faux slip and shine they don't nourish the hair at all.
I am particularly interested in ingredients that will have a good chance of working for my skin or hair based on published research: hydrolysed protein and lauric acid in coconut oil can both be absorbed into the hair shaft, other natural oils are good sources of the fatty acids naturally found in healthy sebum or in the 'glue' holding the cuticle scales together. Aloe vera has study after study showing benefits for skin so no problem if that gets on my hands or scalp from a hair product.