Unless you're giving each customer's meals a nice massage before serving them, your skin condition means nothing from a hygiene POV if you're acting as a server or a host.
I'm reminded of the time I waited 90 minutes on line for Shake Shack (original location, when it first opened) and as I got closer to the front saw that the cashier had a visible and severe herpes outbreak that looked like it wasn't being treated. She kept scratching at her face and then touching peoples' money.