The anomalous behavior I'm reporting isn't just on one site but is showing up on sites running 4.6.12.1 and 4.7 Beta 9.

Member 1 & Member 2 are members of the club, whereas Member 3 hasn't as of yet joined.  None of the members are moderators, as such, none should be able to see the member list.

When I select the "Club Moderators" as shown below, the setting isn't being honored.

There shouldn't be any members listed in the three crossed out boxes.

Unfortunately, I am unable to reproduce this on 4.7 Beta 9 on a test install. Do you have an example URL which we can investigate this further and validate your settings?

I've toggled the third-party "Improved Clubs Ehancement" app off and on over the past few weeks while extensively testing club functionality.  Sometimes I would see the behavior above and sometimes I wouldn't. 

I thought I had disabled the third-party app on all my sites earlier today and it looks like one site (the one that I made the screenshots above) hadn't actually been disabled even though I clicked on it.  Any site where the app is enabled the above behavior presents itself.  The moment I disable the app the above behavior disappears.  I have gone ahead and filed a bug report with the developer.  

Go ahead and close out this support request.

Glad to hear you found the issue at least 🙂