If you google 'skunk-like body odor' or 'sweat smells like skunk,' up come a couple of things that I didn't think of. One was drugs the person is taking -- Adderall is mentioned. Do you regularly take anything? The other is, have you ever been checked for diabetes or kidney problems?
Pretty strange. I guess I'd find a way to bring a sweatshirt or hoody and sit on it. Do you eat a diet that features a lot of something that is known to come through the body chemistry? Like broccoli, cabbage, soy, onions or garlic?
Maybe your body chemicals react in an odd way with the plastic in the chair.
What kind of laundry detergent do you use? It might be the interaction of the detergent smell and the plastic of the chair.
Another thing to try is to use Listerine on your skin, and/or stick deoderant on your hiney.
Talk to a doctor and see if there is any medical condition that is heralded by a strange body smell. Maybe it happens other places too but other surfaces you sit on are more absorbent.