Is exposure to motor oil bad for people?

Yes,

Motor oil is essential to fossil fuel motors. ... Used motor oil contains, benzene, hydrocarbons, gasoline, diesel, antifreeze, and metal shavings from the engine. Frequent exposure and prolonged contact with used engine oil can cause skin rashes, dermatitis, blood anemia, headaches, tremors, and skin cancer. Avoid unnecessary contact with used engine oil. ... Don't keep oily rags in pockets as the oil will seep through overalls etc and affect the skin below.