Firstly, I'm surprised that your ex says he wants to maintain no contact. Typically, it is for the person who has been dumped. What exactly does he hope to gain from it? Unless you have been stalking him, which doesn't seem likely, then it's an unusual step to take.
You are in an awkward situation, and you shouldn't feel pressurised into giving up your sporting activities. You will need to carry out a modified form of no contact. This is usually what people do if they work together, have children, or have joint financial assets.
Keep contact to an absolute minimum and only speak to him if it is absolutely necessary. Same rules apply. Don't stalk him and don't make excuses to speak to him. It's going to be difficult as you will see him on a regular basis. Unless one of you finds a different team, that's all you can realistically do.