The Show Me in #open switch found on the Privacy & Safety page (tap the button in the upper left corner of the screen, tap the Profile tab, scroll down, then tap the Privacy & Safety button) is one way to toggle your profile from Active to Hidden.
When a profile is Hidden, it can no longer be seen by anyone in the #open community when they browse through the app or search via hashtag or username. Setting a profile to Hidden will also disable the ability for that profile to find or view other new profiles in the app (we don’t want invisible lurkers haunting our community!) While hidden, you can still continue chatting with profiles you have already matched with, and the owners of those profiles can still see your profile.
You can access this same functionality from the Solo/Partnered page (tap the button in the upper left corner of the screen then tap the Profile tab, then scroll down and tap the Solo/Partnered button). Here you’ll see a toggle beneath the image in the Solo Profile section, tap this to toggle your profile between Active and Hidden. You can also choose to hide your Partnered profile in the same way: just tap the toggle in the Partnered Profile section on the same page.