It's a known issue FriendsOfFlarum/user-directory#36
I've seen this discussion has just been linked by PeopleInside in the GitHub issue. So it's now cross linked.
I have not yet been able to investigate what the cause is. Feel free to leave comments on the GitHub issue if you identify it, or submit a PR. Changing the z-index via CSS seems like a hack, unless we maybe set a wrong z-index somewhere via the extension itself ?