@mmutonyi
Go to wp-admin > Settings > Buddypress > Pages and check which page is connected in members directory
The page which you will select here will actually work like members directory
This is the problem: If I go to Vibe BP - Settings - Buddypress then disable public profile and disable public member directory then no one can log in.
If you uncheck those boxes then people can log in BUT their profiles are public (anyone on the internet can see their details). It should be possible to disable public profile and public member directory viewing and still let people log in.