Cleaning something is rarely a bad idea. What kind of headgear are we talking about? also - is it your headgear, or community headgear shared in the gym?
Definitely wipe it down thoroughly and definitely use some kind of alcohol or antibacterial. Staph infections are no joke, especially when you have them on your face or head.
Most head gear can -- AND SHOULD -- be cleaned. Check the labels since the exact procedure depends on the construction of the headgear. Leather is harder to clean, but most nylon, synthetic leather, etc, can be cleaned with antiseptic wipes. Foam dipped padded gear can absolutely be wiped down with any antiseptic wipe, or any disinfectant solutions. Bloody gear should certainly be disinfected...