BuddyPress

In BuddyPress, how can you delete the option for users to edit their “Base” profile information?

By default the only “base” information is the username. This can’t be deleted.
Also why to delete when you can hide or give permission ?

For the other field or fiedset YOU added, try some of these plugins

http://wordpress.org/extend/plugins/bp-profile-privacy/

http://buddypress.org/community/groups/bp-privacy/