It is absolutely no problem wearing contact lenses in the gym. While, it should be a wrong choice for having some sport games with contact lenses, such as playing basketball, volleyball, swimming and so on. During the process of sport games, your eyes can be easily hurt by accident, and wear contact lenses could make it worse.
Absolute, you can. You are just not allowed to swim in the pool with contact lenses. Compared to eye glasses, contact lenses can help to avoid being hurt by glasses pieces or frames. But there is also a problem that you need to pay attention to. When you wear contact lenses during your exercise, sweat and something else dirty things are easy to enter eyes result to eye infection. So the best thing to do is no any lenses during playing though it may affect your skills.
Ok, looks like you have been very careful of your eye health right? That is good news actually. So, generally speaking, it would be ok for anyone of us to take sports in the gym with a pair of contact lenses. But what you should know is not to look directly into some tanning lights or strong albums, that would be dangerous to your eye health. And just try not to wear them for much too long during sports hours ok?