Privacy control for profiles is a very frequently asked topic in BuddyPress Community and inside Support questions. By default all BuddyPress Member Profiles are public and can be indexed by Google. BuddyPress Private Community Pro offers a feature to lockdown BuddyPress Component and asks users to log in to go further to check the profile or any other protected details. There is limited BuddyPress community features for Logout users and also based on user role or specific user, e.g. Subscriber can not send Private messages.
BuddyPress Private Community Pro Plugin Introduction
Update on December 31, 2020