Gymnasts use grips which go on your hands for when you do bar work. Do not touch someone elses grips, it is very bad luck if you touched or used someone elses grips. They are molded to your hand so you dont want to mess up the shape. Sometimes you write yourself a message on your grips for good luck. I once wrote go for it on the grips. Most grips are leather which gets supple and bendy.
She thinks the grips are so vital to gymnast performance that it makes sense not to interfere with another persons grips. Touching really will mess up the shape so she believes this superstition is still around because of its practical purpose, keeping your grips in their original form.
Since gymnastics is a very individual sport, it makes sense that people are even more competitive over different aspects of the sport. You can only rely on yourself, so you might be even more particular about anyone sabotaging you. Thus it seems like a logical transition to make even touching other peoples items taboo since it discourages people from even coming near your items.