Can I stop appearing to people nearby?

Yes. In Settings → Account settings → Privacy you can:

• hide yourself from the map, so you don’t appear on it to other people
• hide yourself from nearby users on the Discover page

There’s also a quick toggle on the map itself to instantly turn off your location on the map. That one only affects the map.

You can still join and host linkups, post Shouts and chat with friends while you’re hidden.