Does gymnastics stunt growth or delay puberty in boys or girls?

Competitive. Gymnasts are often small people. Some studies argue that a chronic calorie deficiency compounded by an extraordinary amount of exercise may stunt growth, while others don't. We do know that delayed puberty is common among gymnasts, swimmers and runners, particularly in girls. Hypothalamic amenorrhea is often seen in these girls. Kids in less competitive gymnastics may not have problems.
No. Gymnastics is just another way for children and adults alike to obtain regular exercise and be physically fit. It should not cause problems as you have asked and if you know children having these issues, you should seek further evaluation from your physician.