actually at the track, its no more stress on your car than a good hard run on the street, plus its safer. Lots of people have a bad opinion of racing at the track. Some think its for really bad people, some of our freinds thought of us in the same breath as people who beat up homeless people the first few times we went.
Also its not hard on your car, unlike autox, and rallycross. Its just 15 second (or less hopefully) of hard driving, then you toddle on back along the side road to the pits.
That said, if you have coolant leaks, oil leaks, weak clutch, worn brakes or tires, old plugs, dirty filters etc, yea its not a good idea.
My car had over 220,000 on it when I first went. I was very worried too, but it should be good.