sorry to hear of the passing of your fathers. i understand your concerns. I've worked in the auto business since 82 as a tech, but worked on bicycles and motorcycles well before that. there was very little talk or concerns about such things back then. we were mostly worried about the techs who smoked while working on carbs and fuel filters. yes some of them did that. I've known two trans techs who developed skin problems on their hands, they weren't sure if it was from the stoddard solvent they would clean parts with or the trans fluid. trans fluid is highly detergent, makes your hands soft. and they had problems with their skin peeling away on their hands.
i started using gloves about 20years ago. I've used mechanic gloves, the cloth ones, latex gloves and i tried the nitrile ones, i don't care for the lack of feeling in the nitrile gloves. all take some getting used to. the cloth ones work well till you get them wet with gas, oil or other petroleum products. the latex ones are cheaper but not any better for tactile feel when wet with brake fluid, or oil. i learned to avoid the latex gloves with the powder in them, combined with the constant hand washing and dry winters, my hands would crack and bleed, and ache constantly. the garden gloves are ok, rubber impregnated cloth. i probably use my gloves 90% of the time now. sometimes i reuse them, other times i don't. i'll average between 10 to 20 pairs a day. luckily my boss provides them for us and encourages us to use them. he use to wrench also. but there are times that nothing but plain skin will work for you. when i do clean my hands i'll try to use a rag, but sometimes i'll use brake cleaner, or some other solvent. but i'll wash up with a good hand soap with pumice like beads and a brush. dawn dishwashing detergent is a good choice also, its designed to wash away oil.
now i know some of you wonder how i can work in gloves all day. well, its just like working with oil or grease on your bare hands, you get use to it. my hands do sweat a lot, but i consider that a good thing. i feel it helps drive the natural oils in my skin to the top and drive out the chemicals. at least thats the lie I'm going with till someone comes up with a better one.
thanks for letting me ramble.