A member of a public group should be able to hide that group from their profile, as if it were a private group. There are multiple reasons somebody might want to do this. Here are a couple I can think of:
  1. If a user is a member of many groups, they may want some of those groups to stand out. For example, if you go to a lot of music events, you will end up with many club groups, which could make it difficult for other users to see another group on your profile which is more important to you, such as an event that you organize.
  2. Having group membership as public effectively forces users to display the group to access group events. For various reasons, not all users are equally open about their interests. For example, not everybody would want to have a bottle feeding cafe group in their profile, but others would. This creates a problem for group owners: make the group public, alienating users who don't want the group in their profile, or make the group private, making it difficult for the group to be discovered. People who are normally very private might not want to join many public groups at all.
I've seen on other platforms users have a checkbox on the group settings screen that allows them to hide the group from their profile. It seems like a simple solution.