How can I make it so that people who aren't my friends on Facebook can't see which groups I'm in?
This is similar to this question, but not quite. The linked question asks about keeping things private from my friends, while my question is about keeping things private from strangers.
See Facebook's Help Community for this answer.
Normally, when viewing somebody's Profile, choosing "More >> Groups" will show the Open groups to which that person belongs. However, by editing the Group section of your Profile (via the pencil icon):
... and then clicking Edit Sections:
... one can choose which sections show up in the Profile, and which will not:
Unchecking the Groups item will prevent it from being displayed in your Profile.
Note, however, that individual stories relating to a Group can still appear on your Timeline, in News Feed, or elsewhere on Facebook!
Open Groups (Public) will always be able to be seen by strangers (non FB friends viewing your profile) as well as your friends.
This will help you more: https://www.facebook.com/help/220336891328465
