Is it smart to do bike racing at 60 if fair, thin, family history of osteoporosis?

Sure. Try not to fall down. Cycling is very good cardiovascular and resistance exercise-not especially weight bearing. Weight bearing exercise, e.G walk, jog, tennis, etc. Give additional stimulation to bones. Consider getting a bone density (dexa) test to see how your bones are-got osteoporosis? Indicated with family history, fair, thin, postmenopausal , especially if you have nev(assuming not on hrt.
Enjoy. If it is something enjoy and wear typical protective gear, you should continue to ride. Still take calcium and vitamin d and a baseline bone denisty is inexpensive, safe, and suggested based on your history.
Hammer! I'm assuming you are involved in uscf age group racing. If you have been racing many years the likelihood is your leg bones are in great shape. Have bone density studies done if worried. If you are just starting getting your cardiovascular system checked is in order. Being fair skinned make liberal use of water resistant sun block and check your skin regularly. See you in 55 and over.