For Bulk Processing:
If you update your Options for address processing, you should be able to reject address information and keep the attributes.  If you choose the address saving type as "Add a new address" (which is initial default), this address will be added regardless of field selection, but if you change it to "Update', you should be able to reject the address information and process the attributes.

For Individual Processing:
  1. Uncheck Select All for "Preferred Address" tab and leave Biographical and Attributes checked
  2. Save and Close
  3. Receive Pop up: "There are remaining updates. Do you wish to reject the remaining updates?"-- Click Yes
  4. Process transaction
  5. Receive Pop Up:  "The transaction has unprocessed profile updates. Would you like to process them? Yes No"--Click No to receive the intended result