The below query that could be used in a query action will set a fields privacy.
Code:
INSERT IGNORE INTO `#__comprofiler_privacy` ( `userid`, `type`, `xid`, `rule`, `params` ) VALUES ( '[user_id]', 'field', FIELD_ID, 2, '' )
With the above replace FIELD_ID with the actual ID of the field you want to set default privacy for the user after registration.