This is a big concern for me. As a commuting cyclist, I need to be able to cycle while locked if chastity is going to be a serious commitment for me.
I've cycled up to ninety minutes in plastic, silicone and metal cages without significant issues. Surprisingly, any issues I had were on top rather than down below. With padded cycling pants, and extra undershorts with their own padding, there were no issues at all under my balls. I had a bit of minor pinching up above, which was resolved with a minor adjustment of position.
Showering in work was a bigger problem than the cycling. I think I need speedos or something to stop the cage slipping off.
Living the real life under lock and key