BuddyPress.org

@foresme
1) Activity Privacy: https://wordpress.org/plugins/buddypress-activity-privacy/

2) Profile Privacy: copy over this file https://buddypress.trac.wordpress.org/browser/tags/2.0.1/bp-templates/bp-legacy/buddypress/members/single/profile/profile-loop.php into your active theme folder following this structure wp-content/themes/yourthemename/buddypress/members/single/profile/profile-loop.php

– at the very top of that file, insert:
<?php if ( is_user_logged_in()) : ?>

– at the very end of that file, insert:

<?php else : ?>
<?php echo "<div style='width: 100%; padding: 20px; border: 1px solid #eee; text-align: center; font-style:bold; font-size: 1.3em;'>You have to log in to view this member's profile.</div>"; ?>
<?php endif; ?>

(updated version of danbp’s reply in this post)

@foresme
What membership plugin are you using? Have you tried:
https://wordpress.org/plugins/private-bp-pages/
Full disclosure I am the plugin author.

@foresme
Yes and it also blocks RSS feeds as well from Google. It won’t remove the things Google already indexed but it should prevent any further indexing of your sites activity etc. Just make sure to read the F.A.Q. before activating the plugin.