BuddyPress.org

I’ve encounter the same requirements for a profile field to be editable only by admin that is non-editable by suscribers.
Someone could eventually commit a small plugin that allows this sort of administrative tagging.

Outside of buddypress perspective, I end up using wp_usermeta database table with a call to add_user_meta($user_id, $meta_key, $meta_value [, $unique] ) and when i need the info stored i use get_currentuserinfo()
references :
https://codex.wordpress.org/Function_Reference/add_user_meta
https://codex.wordpress.org/Function_Reference/get_currentuserinfo