Gloves
I might go somewhere and pick up chemical residues at the store or shaking hands with someone. When I come back to my car, I put on layered disposable gloves (five polyethelene food service gloves and one nitrile glove per hand) so that I do not spread chemicals from my hands to the steering wheel and other parts of the car. See my blog post here on disposable gloves.
Seat Protectors
I sometimes pick up strong chemicals on my clothes if I sit on a chair with chemical residues. I use seat protectors (a piece of plastic or other relatively hard material) so that I do not contaminate the seat of the car. I can just put the seat protectors in the dishwasher if they get chemicals on them. Towels can work as seat protectors as well but I prefer the harder material because some chemicals on the seat can go right through a towel but generally not through a thick piece of hard plastic.
Containers for Items
I often put groceries and other items into plastic or metal containers, such as a Granite Ware stockpot (see post here) or a plastic bin. That way, if there are chemicals on the items, they will not spread to the seat of the car. I use containers that are barely small enough to fit in our dishwasher so that I can wash them if they acquire chemical residues.
Steering Wheel Protectors
There are disposable plastic steering wheel protectors that one can buy. I haven’t tried this, but that might be a good idea when you need to take your car to the shop. I just wrapped my steering wheel with aluminum foil with duct tape on the outside. If my steering wheel gets very strong chemicals on it, I will just remove the foil and tape.
The back of my car has some extremely strong chemicals on it so I covered it with sheet metal:
