BuddyPress.org

@jonnycardel so you want to delete that whole section with the avatar, login, AND logout? Open up sidebar.php https://trac.buddypress.org/browser/tags/1.2.6/bp-themes/bp-default/sidebar.php starting at line 8 where Is_user_logged_in to line 56 with php endif; deals with the avatars, login and logout. If you do not want them, delete the block.

@jonnycardel if you’re using a child theme of bp-default, then copy over sidebar.php from bp-default theme to child theme folder. If it’s only the Log Out link you want to delete, then delete this line from your sidebar.php
<a class=&quot;button logout&quot; href=&quot;"></a>